We construct the Carrollian limit of NS--NS and heterotic supergravity through an ultra-relativistic expansion of the fields. An appropriate scaling of the dilaton renders the measure finite and compensates the divergences arising from the NS-NS supergravity Lagrangian, giving a finite action as $w\rightarrow\infty$. We then extend the construction to heterotic supergravity (neglecting fermions) by incorporating the non-Abelian gauge field together with the Green--Schwarz (GS) mechanism. The resulting theory contains a finite gauge sector consistently coupled to gravity, and the GS mechanism for the Carrollian 1-form field can be trivialized imposing field redefinitions. Then, we investigate the Carrollian equations of motion by both expanding the relativistic equations and deriving them from a variational principle. We also show that the leading $\alpha'$-corrected $\hat{\rm Riem}^2$ contribution remains finite under a rescaling of the string parameter $\alpha'\rightarrow \frac{\alpha'_c}{w^2}$, opening further research towards the full four-derivative effective action. Finally, we discuss the potential connection with the worldsheet formalism of the Carrollian string theory.

We show that solving the abelian part of the local anomaly cancellation conditions for a 4-d gauge theory whose gauge Lie algebra has an abelian summand with rank $K \geq 1$ is equivalent to the problem in algebraic/arithmetic geometry of finding $(K-1)$-dimensional projective linear subspaces of a cubic hypersurface over the rational numbers, where the cubic is determined by the data of the semisimple summand and the representation thereof carried by the Weyl fermions. We then use this reformulation to solve a variety of examples with rank 2. The simplest non-trivial example from physics, namely gauge Lie group $U(1)^2$ and six fermions, nevertheless has a rich (and well-studied) geometry: it corresponds to the Fano variety of lines in the Segre cubic primal threefold. This is a surface with 15 irreducible components that are planes (which correspond to lines lying in the 15 planes in the Segre cubic primal and which give rise to non-chiral fermions) and 6 components that are split del Pezzo surfaces of degree 5 (which give rise to chiral fermions). These components are all rational varieties, enabling all solutions to the anomaly cancellation conditions to be parametrized and their collective properties (e.g. their topology and asymptotic distribution) to be described.

Thanks to bosonization, bosonic lattice models can offer a lattice regularization of chiral fermions. We construct chiral lattice fermion operators in the 2D modified Villain scalar model and evaluate their correlation functions. This microscopic bosonic model has an ultra-local action and an ultra-local symmetry that realizes the fermionic chiral symmetry under bosonization. The reconstructed lattice Dirac operator has no doublers, but is consistent with the Nielsen-Ninomiya theorem because it turns out to be non-local. The non-locality of this derived quantity at finite lattice spacing does not pose any obstructions to gauging the non-anomalous symmetries of the model, which is itself ultra-local.

Bern-Carrasco-Johansson relations are helicity-independent constraints among the partial amplitudes of tree-level processes containing gluons and possibly also matter fields. They are a consequence of color-kinematic duality, but alternatively can be derived using the color-factor symmetry of tree-level amplitudes. We use recursive perturbiner methods to present a general, streamlined proof of the color-factor symmetry of all tree-level amplitudes containing an arbitrary number of fundamental spin-zero or spin-one-half matter fields and at least one gluon.

We use the auxiliary polarization spinor formalism together with superspace techniques to construct a complete and minimal list of 3-point invariant structures in three-dimensional superconformal field theories (SCFTs) with $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal symmetry. The existence of non-abelian $R$-symmetry for $\mathcal{N}=3,4$ gives rise to novel invariant structures built from the antisymmetric invariant tensor. These invariants are used to enumerate the structural form of spinning 3-point correlators of general as well as conserved spinning superfield operators in 3d SCFTs. For conserved operators, we find that the $\mathcal{N}=3$ correlators are fixed upto one parity-even and one parity-odd structure, while $\mathcal{N}=4$ conserved correlators admit two parity-even structures and one parity-odd structure, with the second parity-even structure associated with mirror symmetry breaking.

We proceed to construct a non-Abelian dual pair for the $AdS_2 \times H^2 \times H^2$ background by applying the non-Abelian T-duality (here as Poisson-Lie T-duality on a semi-Abelian double). By using a certain parameterization of the $6$-dimensional Lie group ${A}_2 \otimes {A}_2 \otimes A_2$ we construct the original $\sigma$-model including the $AdS_2 \times H^2 \times H^2$ metric in the absence of $B$-field. It is shown that the dual background constructed by means of the Poisson-Lie T-duality is supported by a $B$-field and a metric whose contains a physical singularity. By studying the behavior of the dual spacetime at small $(r , y, u)$ coordinates, we show that the dual metric with a zero field strength and a non-trivial dilaton field make up a solution for the vanishing of the one-loop beta-function equations. Furthermore, at large $(r , y, u)$, it is shown that the $AdS_2 \times H^2 \times H^2$ solution is preserved under the non-Abelian T-duality. Finally, using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality for the gluing matrix which locally defines the properties of the D-brane, we find seven different cases of the gluing matrices for the $AdS_2 \times H^2 \times H^2$ $\sigma$-model and its dual pair. In this way, it is found a symmetric duality action on the branes linking together in a duality chain.

We investigate Krylov spread complexity for states evolving under time-dependent Hamiltonians. For periodically driven systems, we formulate the problem within Floquet theory and show how the Magnus expansion provides a systematic approximation when the Floquet Hamiltonian is not available in closed form. We then extend this framework beyond periodic driving and demonstrate that, in addition to the globally truncated Magnus expansion, a piecewise Magnus expansion provides a reliable method when the global expansion loses convergence or accuracy. Our results provide practical tools for analyzing complexity growth in a broad class of time-dependent quantum systems.

We develop a microscopic quantum membrane paradigm from the matrix quantum mechanics of black holes [1]. It was proposed that a quantum black hole is described by a fuzzy sphere together with a half-filled Fermi sea of horizon partons. We show that the topology of the fuzzy sphere induces a Berry monopole, providing a microscopic origin for the monopole appearing in the tunneling description of the decay of quantum black hole. Because the partons couple to the fuzzy sphere as fundamental degrees of freedom, they are sensitive to this monopole and form Lowest-Landau-Level (LLL) states rather than ordinary propagating two-dimensional fermions. Their guiding-center dynamics generates Ohmic, Hall, and polarization currents on the horizon. To couple these currents to an external electromagnetic field, we introduce a two-block matrix configuration comprising black-hole, environmental, and bifundamental link sectors. Off-diagonal link modes become tachyonic near the fuzzy sphere and condense, dynamically locking the horizon gauge field to the boundary value of the external Maxwell field. The parton current thereby becomes a physical boundary source for the exterior field. Our construction replaces the fictitious membrane of the classical paradigm with a dynamical quantum membrane populated by microscopic LLL degrees of freedom. The resulting boundary condition generalizes the classical ingoing membrane condition and yields explicit quantum, frequency-dependent, and helicity-dependent corrections, offering a possible probe of the microscopic quantum structure of the horizon.

We study a four-qubit product-EPR holographic code whose reconstructing region contains matter and one leg of a geometry bond. Seven deformations compare local, bipartite, bond-stabilizing, and bond-moving operators. Exact spectra show that only matter-controlled bond motion produces a leading quadratic logical-state dependence of the boundary entropy. We select one state-independent physical recovery by optimizing coherent information of the channel Choi state. A separate semidefinite program maximizes entanglement fidelity over all channels. At fixed coupling the physical recovery attains that optimum to numerical precision, while recovered-entropy subtraction leaves a nonzero variational proto-area response. Total stabilizer Renyi magic is also nonzero for deformations with no boundary response, so it does not characterize the effect. Projecting the exact stabilizer-Renyi quadratic form away from pairwise Pauli tangents defines a leading-order boundary witness. Its global convex minimum is positive for the bond-moving deformation and zero for the six comparisons. For the reference-matter-geometry resource partition, however, pairwise tangents span the full projective tangent space at the product-EPR base, so the witness vanishes for every Hermitian deformation. A two-bound extension retains this degeneracy but exhibits a split-geometry structural residual and a logical-state-dependent cut switch. These results establish a finite-code witness, not a universal magic law or continuum gravitational dynamics.

The one-loop effective Lagrangian of quantum electrodynamics for dyons (dQED) with a $U(1) \times U(1)$ gauge symmetry is derived using the Schwinger proper-time method. We identify the analog of the Schwinger pair-production limit and compute the corresponding nonlinear equations of motion. The electromagnetic response of the model is analyzed by linearizing the equations of motion around a purely magnetic background. From the resulting plane-wave solutions, we obtain the effective permittivity and permeability tensors, along with the associated dispersion relations and refractive indices for parallel and perpendicular polarization modes. The refractive indices involve hybrid superpositions of both gauge sectors, as illustrated in the symmetric case $q_{(1)} = q_{(2)}$. In this background, the model exhibits vacuum birefringence, indicating that the quantum vacuum behaves as an anisotropic medium. All results consistently reduce to the standard Euler-Heisenberg predictions of QED when the magnetic charge vanishes.

Krylov complexity is a powerful diagnostic of quantum dynamics, with clear connections to other measures of quantum chaos and operator growth. One such measure is the Loschmidt amplitude, defined as the overlap of initially identical states evolved under two slightly different Hamiltonians. Its decay in certain systems is controlled by the classical Lyapunov exponent. Using the algebraic properties of the Krylov complexity operator, we express Krylov complexity as the derivative of a Loschmidt amplitude whose perturbation is parameterized by an angular variable $\phi$. This formulation allows us to define a spectral propagator that encodes the entire complexity distribution, which we characterize for specific types of systems. We study the two-dimensional quantum geometry spanned by time and $\phi$ where the original and deformed trajectories reside, demonstrating that Krylov complexity is upper-bounded by its volume. We also express the time derivative of Krylov complexity in terms of a distinct Loschmidt amplitude. Depending on the growth of the Lanczos coefficients, the perturbation term in this amplitude can be truncated. We propose that the strength of this perturbation provides a classification scheme for Krylov complexity dynamics and relate it to the $\phi$-derivative of the spectral propagator. Using this analytical framework, we derive general relations between the time-dependence of the survival amplitude and Krylov space measures.

It is widely believed that global symmetries cannot exist in a consistent theory of quantum gravity. A prominent mechanism underlying this expectation is provided by gravitational instantons or Euclidean wormholes, whose contributions to the Euclidean path integral generates local symmetry-breaking operators in the effective action with couplings parametrized by the $\alpha$-parameters $\overrightarrow{\alpha}=(\alpha_1^{},\alpha_2^{},\cdots)$. The appearance of these $\alpha$-parameters is often taken as evidence that wormholes explicitly break global symmetries. In this paper, we argue that this conclusion is premature. The fate of the symmetry is determined by the ensemble average over these $\alpha$-parameters. We show that, under broad situations, this average can be sharply dominated by the symmetric point $\overrightarrow{\alpha}=0$, while contributions from other symmetry-breaking critical points $\overrightarrow{\alpha}\neq 0$ are typically suppressed by a doubly exponential factor $\exp(-e^{2S_{\rm ins}})$, where $S_{\rm ins}$ is the instanton action. In particular, standard $\mathrm{U}(1)^{}$ Peccei--Quinn models fall into this class, implying that the conventional axion quality problem does not arise in the wormhole-induced effective theory. Our analysis is formulated for general $\mathrm{U}(1)^{}$ $p$-form global symmetries.

We consider the classical satellite and splice constructions of knot theory from the perspective of link-complement states in three-dimensional topological quantum field theory (TQFT). These states are prepared by a TQFT on a link-complement manifold, namely a manifold with multiple disjoint torus boundaries, obtained by removing a thickened link from a closed ambient three-manifold. In this setting, satellite and splice constructions are realized by gluing manifolds along torus boundaries, and the TQFT assigns to these building blocks multilinear operators acting on the corresponding torus Hilbert spaces. We give explicit prescriptions for these operators and show how they can be used to build link-complement states. This construction is closely related to the JSJ decomposition of link-complement manifolds. While splicing builds manifolds by gluing along tori, the JSJ decomposition cuts a manifold along essential tori into canonical pieces. From the TQFT point of view, this expresses a link-complement state as a network of elementary operators associated with the JSJ pieces. We illustrate this framework by studying the entanglement entropy of Seifert-fibered link complements, Hopf-chain complements, and complements of Whitehead-doubled Hopf chains, showing how their different JSJ structures lead to distinct entanglement patterns.

Recent analyses of Proca theories with non-minimal curvature couplings have uncovered an additional scalar degree of freedom with an identically vanishing propagation speed, $c_s^2=0$, signaling a scale-dependent strong-coupling problem. In this {\it Letter}, we show that an additional derivative interaction can lift this zero-speed degeneracy and restore a non-degenerate quadratic dynamics for the scalar perturbations. In an open region of parameter space, the scalar kinetic matrix is positive definite and the high-frequency propagation speeds are real and positive. At quadratic order, this removes the specific signature of strong coupling associated with the $c_s^2=0$ mode. We also uncover a non-uniform limit as the temporal vector condensate approaches zero: at fixed nonzero $A_0$, the formal extreme-ultraviolet regime develops a ghost, while the kinetic structure of the exactly vanishing-condensate branch is different. The momentum scale at which this ghost appears is pushed toward increasingly high values as $A_0\to0$. Whether the ghost scale ultimately lies above the EFT cutoff depends on an independent determination of the EFT cutoff. Finally, we identify a stable de Sitter fixed point with $A_0\neq0$, surrounded by a finite region in which the scalar no-ghost and high-frequency stability conditions remain satisfied.

In this paper, we discuss the conjugate boundary condition (CBC), which has recently been studied as a way of realizing a Majorana fermion within a compactified five-dimensional theory ($\mathcal M^4\otimes S^1/Z_2$). The Majorana fermion which plays a crucial role in the seesaw scenario arises as a zero mode (lowest mode) by imposing the CBC. Although each nonzero Kaluza-Klein (KK) mode is also naively expected to be described by two Majorana fermions, we show by direct calculation that they can be combined into a Dirac spinor in the free theory or up to the level of the quadratic term in the Lagrangian. This difference comes from the fact that an accidental U(1) symmetry exists in the KK mode sector, though such a symmetry does not appear in the zero mode sector. We also point out that the compatibility between the CBC and the axial U(1) transformation plays a crucial role in the diagonalization of the KK mode. We also investigate interactions compatible with both the CBC and the chiral orbifold projection. We find that a nontrivial bulk interaction between a CBC fermion and a chiral-orbifold fermion is allowed. As an application, we construct an extended seesaw scenario by utilizing both boundary conditions and such nontrivial bulk interactions. The resulting seesaw scenario has a different property in contrast with the conventional extended seesaw scenario; namely, the above new non-trivial interactions cause lepton number violation (LNV), while the Majorana mass term in our model does not violate lepton number.

We derive the Belinfante--Rosenfeld symmetrization procedure from the metric-affine conservation law by means of an affine lift of flat-spacetime field theories. Following minimal coupling to an independent affine connection, variation of the action with respect to the connection defines the hypermomentum current. Taking the flat-spacetime limit of the resulting conservation law, we recover the Belinfante--Rosenfeld relation, with the divergence of the hypermomentum current reproducing the Belinfante improvement term. We thoroughly study the form of the couplings with this property and their physical significance. The construction is illustrated for Quantum Electrodynamics and Quantum Chromodynamics.

We use the large $N$ critical point formalism to examine the interplay of supersymmetry and chiral symmetry on the location or otherwise of multiple zetas in the renormalization group functions of several related field theories. In particular we determine that the anomalous dimension of the matter field of the Lagrangian corresponding to the bosonic sector of the $O(N)$ Wess-Zumino is free of multiple zetas to $O(1/N^3)$.

In this manuscript, we propose a novel topological framework based on the heat capacity of black holes to investigate the topology of thermodynamic multicritical points. We construct a two-dimensional thermodynamic vector field whose isolated zeros correspond to the critical points of the system. The local topology of each critical point is characterized by its Brouwer degree, which serves as a locally conserved topological quantity. Applying this formalism to several AdS black hole solutions, we demonstrate that each system possesses a globally conserved topological charge. Although the number of thermodynamic critical points changes as the thermodynamic parameters are varied, the total topological charge remains invariant throughout the evolution. We show that these topological transitions are governed by the creation or annihilation of topologically neutral defect pairs carrying opposite Brouwer degrees. Our results provide a unified topological framework for understanding the emergence, evolution, and classification of thermodynamic multicritical points in black hole systems.

In this paper, we considered two-particle variants of the N-extended Euler-Calogero-Moser and Calogero models. Due the translation invariance, the center of mass can be decoupled (together with the corresponding fermions), leaving us with specific superconformal mechanics. Additional bosonic variables (spin variables) can easily be incorporated into the supercharges and the Hamiltonian. In the case of the Euler-Calogero-Moser model, the supersymmetry in the two-particle cases admits an unexpected extension from Osp(N|2) to SU(1,1|N) superconformal symmetry. The case of the Calogero model leads to purely Osp(N|2) superconformal mechanics. The way to get rid of the well-known problems along this path is to have a higher number of fermions present in the system.

We present an exact solution describing multi-rotating black holes in 4D Einstein-Maxwell-dilaton theory, which can be obtained from 5D Kaluza--Klein theory via dimensional reduction. The solution represents a multi-centered configuration of rotating black holes carrying both electric and magnetic charges, with each black hole possessing a non-aligned angular momentum. This work generalizes our previous solution for black holes with aligned angular momenta to the more general case of non-aligned angular momenta. It includes, as special cases, the Majumdar--Papapetrou solution, the recent multi-centered rotating black hole solutions of Teo and Wan, and our previous solution with unequal electric and magnetic charges. The resulting spacetimes are free of curvature singularities and closed timelike curves, both on and outside the horizons, provided that the magnitude of the spin angular momentum of each black hole remains below a certain upper bound.

We develop a non-nested Bethe ansatz description of rational $\mathfrak{gl}_\ell$ spin chains in the vector representation. Starting from the quantum spectral curve and the separation-of-variables framework, we derive closed systems of Bethe equations involving only the momentum-carrying Bethe roots. The construction is worked out explicitly for the $\mathfrak{gl}_3$ and $\mathfrak{gl}_4$ spin chains and then generalized to arbitrary rank. A central result of this work is the identification of a recursive hierarchy associated with the fundamental transfer matrices. The hierarchy is generated by regularity conditions of the lower transfer matrices and closes through a universal rank-$\ell$ equation $\mathcal{R}_{\ell}=0$. This equation replaces the final level of the conventional nested Bethe ansatz and eliminates all auxiliary Bethe roots. Consequently, the complete spectral data of an eigenstate are encoded solely in the first Baxter polynomial $Q_{1}(u)$. We further obtain explicit expressions for the eigenvalues of all fundamental transfer matrices in terms of the momentum-carrying roots alone. The resulting formulation provides a compact characterization of the spectrum of rational $\mathfrak{gl}_\ell$ spin chains and reveals a direct connection between the quantum spectral curve, transfer-matrix fusion relations, and a truncated $Q$-system underlying the non-nested description. Finally, we investigate the quasi-classical (Gaudin) limit of the non-nested Bethe equations. For the $\mathfrak{gl}_3$ spin chain, we show that the leading non-trivial contribution gives rise to Gaudin equations whose pole-free form naturally defines a scalar third-order $\mathfrak{gl}_3$ oper.

We study timelike entanglement entropy and timelike subregion complexity in localized black holes with asymptotic AdS3*S3*T4 geometry, focusing on the black-pole solution. Unlike the BTZ solution, the black pole exhibits a nontrivial dependence on the internal sphere through the functions $K_y(r,\theta)$ and $G(r,\theta)$. Both observables are constructed from spacelike and timelike Lorentzian branches, but they probe the geometry in different ways: timelike entanglement yields a complex lifted area, while timelike complexity gives a real, finite renormalized volume. We employ a localized timelike prescription in which the branch profile is built at an angular label $\theta_0$ and subsequently lifted over the physical internal angle $\theta$. In the large-$r$ regime, the leading angular dependence drops out, recovering the expected short-interval behaviour. In the exact black-pole geometry, the temporal families become non-monotonic, making a fixed-boundary-interval selection essential. As the boundary interval increases, the selected branches move inward and become sensitive to the localized cap-horizon transition region. These results demonstrate that timelike Lorentzian observables probe localized-geometry effects that are absent in BTZ and in the leading large-$r$ description.

We set up a bootstrap workflow to study four-point conformal integrals in position space, using leading singularities, single-valued multiple polylogarithmic ansätze and boundary data from expansion by regions. These four-point conformal integrals are general in the sense that they are generated by the four-point projections of all possible $f$-graphs, including all non-planar $f$-graph sectors. For three-loop cases, fourteen of the fifteen inequivalent integrand basis can be directly calculated by \texttt{HyperlogProcedures} and the last one is fixed by Gram identity. Then we concentrate on how far the bootstrap workflow can go for four-loop cases, though it works for three-loop cases as well. We show that integrals with several leading singularities can be made tractable by decomposing them into pieces with simpler cut structure. Some four-loop integrals which can not be calculated or very hard to be calculated by other methods for now are obtained in this way. We also provide a package with skill files which is suitable to be read and used by current AI models.

We study the low-temperature expansion of the disk partition function $Z(\beta)$ of the double-scaled SYK model (DSSYK) at fixed coupling $\lambda=2p^{2}/N$, where $N$ is the number of Majorana fermions and $p$ is the number of fermions in each interaction term, both taken to infinity. We show that the exact Bessel-function representation of $Z(\beta)$, expanded at large argument (corresponding to low temperature), can be organized in terms of the classical ring of quasi-modular Eisenstein series $E_{2},E_{4},E_{6}$ and their differential identities. Exploiting the modular $S$-duality properties of this ring, we derive the semiclassical (small $\lambda$) low-temperature expansion of $Z(\beta)$, splitting it into a perturbative tower and a non-perturbative sector controlled by $\widetilde q=e^{-4\pi^{2}/\lambda}$. At each order in $\widetilde q$, we determine the non-perturbative correction in closed form up to second order in $\lambda$; the resulting series resums into a compact expression in the same Eisenstein series, extending previous semiclassical results beyond their strict $\beta\to\infty$ limit. We further show that this entire structure follows from a single, exact differential equation coupling a modular derivative to derivatives with respect to temperature. Finally, we prove that the non-perturbative sector of $Z(\beta)$ is exactly supported, to all orders in $\lambda$, on the same exponents as the on-shell actions of known bilocal-Liouville saddles of the DSSYK Schwarzian limit, pointing to a well-defined bulk origin for these non-perturbative corrections.

In this paper, we study codimension-two holography in a de Sitter (dS) wedge setup, based on the idea of wedge holography. We consider a $d+1$-dimensional Anti-de Sitter (AdS) bulk spacetime bounded by two end-of-the-world branes with $d$-dimensional de Sitter geometry. We propose that this configuration is holographically dual to a conformal field theory (CFT) living on a $d-1$-dimensional sphere. Our computations of the partition function and holographic entanglement entropy support this duality and indicate that the dual CFT is non-unitary. We also analyze the mass spectrum in dS wedge holography. We verify the first law of entanglement entropy within this framework. Finally, we make use of the island prescription to study the Page curve in a simplified model within our dS wedge holography framework.

Recent observations from the Atacama Cosmology Telescope (ACT) point to a scalar spectral index in tension with the predictions of Starobinsky inflation. Two main strategies have been proposed to reconcile Starobinsky inflation with these data: (i) including higher-curvature operators in the gravitational action, and (ii) modifying the post-inflationary reheating dynamics. We critically re-examine both approaches. When higher-curvature corrections are included, dimensional-analysis arguments allow introducing a second mass scale suppressing higher-dimensional operators, resulting in a one-coupling, two-scale effective theory. We show that fitting the ACT data drives this class of effective theories toward a regime of stronger sensitivity to UV physics, potentially implying fine-tuning of the inflationary observables. We illustrate our general point with two concrete models, namely no-scale supergravity and metric-affine gravity, showing that they provide different realizations of the same underlying $f(R)$ theory. On the reheating side, requiring the CMB modes to re-enter the horizon before recombination leads to stringent constraints on the reheating equation of state, and fitting the ACT data favors an exotic reheating phase with $\omega_{\rm reh} > 1/3$, incompatible with inflaton oscillations about the minimum of the standard Starobinsky potential. Finally, we explore the possibility that a phase of cosmological stasis, driven by a tower of decaying massive states, could play the role of the post-inflationary epoch. We find that accommodating ACT-preferred $n_s$ in this setup requires a tower of states with negative energy density. Taken together, our results suggest that reconciling Starobinsky inflation with the ACT data demands ingredients that are challenging to motivate from the perspective of UV-complete theories, undermining the minimality of the original Starobinsky model.

In AdS/CFT, one often finds claims along the lines that ``spacetime emerges from entanglement." This paper argues that behind these general statements hide three distinct emergence claims about, respectively, metric, gravitational dynamics, and topological connectivity. Thus, despite being advertised with the same terminology, these results are not about the same spatiotemporal aspects. They can therefore not just be grouped as evidence for one unanimous conclusion, though they do point in similar directions. The paper also investigates whether the three emergence claims satisfy two of the necessary conditions for emergence: Determination and novelty. The paper argues that none of the emergence claims satisfies the determination condition: More than entanglement is needed to furnish the emergence basis. Besides entanglement, the emergence basis for the bulk metric must include the induced metric on the boundary. Thus, this claim might not satisfy the novelty condition for emergence that the emergent should be novel as compared to the emergence basis. Likewise, the emergence basis for topological connectivity seems to include connectivity whereby this emergence claim is also questionable. The paper concludes that only gravitational dynamics is novel compared to the fully furnished emergence basis.

The established $d=5$ ALP effective Lagrangian describes the interaction of scalars with approximate shift-symmetry which carry no Standard Model (SM) charges with SM fields. It implicitly assumes that ALPs are not charged under any symmetries of the dark sector. In this paper, we remove this assumption. For ALPs carrying conserved dark charges, no $d=5$ ALP effective interaction to SM particles is possible. We build the effective Lagrangian for these darkly charged ALPs stemming from a general breaking pattern, and we show that the lowest-order shift-symmetric effective Lagrangian contains just two $d=6$ operators coupling ALPs to SM particles. We explore the model-independent phenomenological implications of these interactions, as well as the question of whether the dark matter observed in the Universe may consist of darkly charged ALPs. We identify higher order operators of the effective field theory, and determine which types of dark symmetry groups can seed darkly charged ALPs. Illustrative examples of ultraviolet completions which result in darkly charged ALPs at low-energies are provided as well. The darkly-charged ALP scenario can be generalized by including dark gauge interactions. In this paper, we have considered only the case with no such interactions.

Extra-dimensional QCD axion is well motivated by string compactifications and enjoys enhanced protection against quality-violating effects. If present during inflation, however, its quantum fluctuations generate isocurvature perturbations that strongly constrain the inflationary scale. We propose a dynamical suppression mechanism in warped five-dimensional models, where a radion-inflaton coupling sets the radion minimum at small inter-brane separation during inflation, temporarily enhancing the effective four-dimensional axion decay constant. After inflation, the radion minimum shifts to larger separation, restoring the standard QCD axion window. In a warped orbifold GUT with Goldberger-Wise stabilization, this mechanism can satisfy CMB isocurvature bounds while allowing substantially higher inflationary scales than in conventional pre-inflationary axion cosmology.

We study scalar and vector bosons in the Bonnor--Melvin--$\Lambda$ spacetime within the Duffin--Kemmer--Petiau (DKP) formalism. By employing Umezawa's projection operators, we separate the physical spin-0 and spin-1 sectors and derive the corresponding exact second-order equations in the full curved spacetime, without relying on the conical approximation. For the scalar sector, the radial equation reduces to a Schrödinger-like equation with a trigonometric Pöschl--Teller effective potential. In the vector sector, the longitudinal mode is governed by the same effective potential, whereas the transverse polarizations are described by generalized trigonometric Pöschl--Teller potentials. Because the me\-tric function vanishes at a discrete set of radial points, the radial dynamics is naturally formulated as a singular Sturm--Liouville problem on a fundamental interval, with the physical radial domain fixed by the Friedrichs self-adjoint extension of the corresponding singular radial operators. As a result, all physical sectors exhibit purely discrete radial spectra, and their eigenfunctions are obtained in closed form. These results provide a unified exact treatment of scalar and vector bosons in the Bonnor--Melvin--$\Lambda$ spacetime, complement previous analyses based on the conical approximation, and clarify the role of the global geometric structure of the background in shaping confinement and spectral properties.

We compute the fermion-photon vertex in QED in the presence of a constant and uniform magnetic background up to one-loop order. We show that even at tree-level, the vertex is modified due to the loss of Lorentz invariance induced by the magnetic field, thus breaking into longitudinal and transverse pieces. Moreover, the radiative corrections induce the emergence of a rich tensor structure that includes the anomalous magnetic moments in the transverse, parallel, and mixed transverse/parallel directions. We concentrate on studying one of these anomalous magnetic moment components, the one in the purely transverse direction. We find the selection rules for transitions between a few low-lying Landau levels and show that the amplitudes for transitions from an initial to a final Landau level differ by a sign from the reverse process due to the loss of time reversal invariance induced by the presence of the field. Contrary to the vacuum case, the amplitudes are, in general, complex, and the phase factor can be interpreted in terms of a finite life-time of the decaying state. For the anomalous magnetic moment in the purely transverse direction, transitions between states occupying both the lowest Landau levels are forbidden. Moreover, for the computation of the allowed transitions, we find that it is not necessary to include a photon mass since the magnetic field acts as an infrared regulator.

We show that relativistic theories with purely relaxational excitation spectra, such as kinetic theory and transient hydrodynamics, naturally endow the dispersion plane $\{i\omega,ik\}$ with a Lorentzian geometric structure analogous to that of the Minkowski plane $\{t,x\}$. In this picture, timelike future-directed, timelike past-directed, and spacelike directions correspond respectively to relaxation-like, unstable-like, and evanescent-like modes. Under mild structural assumptions on the underlying theory, causality constrains dispersion relations to follow spacelike trajectories on the plane. This geometric viewpoint recasts longstanding problems in relativistic matter physics as elementary geometric ones that can often be solved graphically. As applications, we derive universal constraints on dispersion relations, deviations from time dilation, the observer dependence of spectral hierarchies, the regime of validity of hydrodynamics in boosted frame, the maximal allowed diffusivity and viscosity of relativistic media, and the presence of non-hydrodynamic branch cuts in kinetic theory.

Anyons in $2+1$ dimensions are not only characterized by exotic braiding statistics but also by intricate fusion properties. Two anyons may fuse into multiple topological charge sectors, and associativity of fusing three anyons to produce a fixed charge sector is governed by $F$-symbols. While braiding invariants, such as the modular data, are typically complex valued, a complete description of general anyon models requires understanding the arithmetic properties of its fusion associativity data as well. The $F$-symbols for many of the most common $2+1$d topological orders, including all Abelian anyon models as well as Fibonacci and Ising anyons, can be made real valued. We show this phenomenon is not universal by exhibiting braided fusion categories whose $F$-symbols cannot be made real. We call such $F$-symbols \lq\lq inherently complex." The examples we study lack a charge-conjugation symmetry and our results are therefore consistent with the converse of a statement proved in a companion work linking real $F$-symbols in braided fusion categories with the existence of a suitable charge-conjugation symmetry. We analyse the smallest-rank braided fusion categories we know of with inherently complex $F$-symbols: ${\rm Rep}(\mathbb{Z}_7\rtimes\mathbb{Z}_3)$ and ${\rm Rep}(\mathbb{Z}_5\rtimes\mathbb{Z}_4)$. Consequently, the corresponding $\mathcal Z({\rm Rep}(\mathbb{Z}_7\rtimes\mathbb{Z}_3))$ and $\mathcal Z({\rm Rep}(\mathbb{Z}_5\rtimes\mathbb{Z}_4))$ anyon models also have inherently complex $F$-symbols. Our presentation connects these examples with recent results on classifying anyons beyond modular data.

We study the motion of massive (un)charged test particles in space-times of electric and dyonic black holes which carry scalar hair. We determine the stable and unstable circular orbits and discuss the collision of massive test particles. In particular, we aim at demonstrating how the presence of the scalar hair of the black hole changes the circular orbits and particle collisions, respectively, as compared to the Reissner-Nordström (RN) space-time. We find that in the presence of scalar hair, up to four circular orbits (two unstable and two stable) as well as static orbits with $L=0$ can exist. Particle collisions can generate infinite center-of-mass energy when at least one of the particles is charged, very similar to the RN case. We find, however, that the value of the charge at which this divergence happens depends on the value of the scalar field on the horizon.

Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology of Schwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction \(\eta E^3/E_P\). Enforcing physical constraints (\(S'(r_h) > 0\), \(T > 0\)) via the entropy-geometry correspondence, we find a single unstable branch with \(w = -1\) and \(W = -1\) for both signs of the correction parameter. A second root suggesting stability (\(w = +1\)) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.

A photon coupled non-minimally to the Weyl tensor propagates differently in its two linear polarization states: the vacuum around a black hole becomes a birefringent medium. On a Schwarzschild background the coupling $\alpha$ splits the photon sphere and the critical impact parameter of the two polarizations, producing a double shadow and a polarization-dependent photon ring; the two shadow edges separate by $62\%$ of the shadow radius at $\alpha/M^2=0.75$. We compute a unified set of wave-optical and geometric-optical observables for both polarizations across a range of $\alpha$: greybody factors, absorption cross sections, differential cross sections and their glories, a backward birefringence signal, shadows, photon rings, and null trajectories. The two-polarization scattering matrices are extracted with a Riccati--Hankel matching scheme that keeps the phase-sensitive observables reliable, and the geometric-optics chain is cross-validated with three independent ray tracers. The cleanest diagnostic is the backward signal: it is protected by parity and vanishes identically at $\alpha=0$.

We construct a new family of asymptotically flat static and rotating regular black holes characterized by a Minkowskian core and a finite two-horizon structure. The solutions are obtained within the framework of gravitational decoupling and provide an analytically tractable realization of non-singular black hole geometries with a regular interior and well-defined asymptotic properties. We investigate the optical appearance of the rotating spacetime through shadow observables and ray-traced images of geometrically thin, optically thin accretion disks. Despite the substantial differences between the interior geometry of these solutions and that of singular black holes, their optical signatures are found to remain remarkably close to those of Schwarzschild and Kerr spacetimes with the same asymptotic parameters. Our results show that markedly different black hole interiors may lead to nearly indistinguishable optical appearances, highlighting the challenges of probing the internal structure of compact objects using current shadow and imaging observations.

I develop a Hamiltonian framework for ${\mathbb Z}_k$ $p$-form gauge fields on arbitrary oriented cell complexes in arbitrary dimensions. Gauge qudits are defined by $p$-cells, charged boundary qudits by $(p-1)$-cells, Gauss-law generators by boundary map $\partial_p$, and magnetic checks by $\partial_{p+1}$. The same cellular structure produces local dressed Wilson operators, and at $k=2$ a Calderbank-Shor-Steane check complex relevant to quantum error correction. I then specialize to $p=2, k=2$, where the magnetic 3-cell term is absent and the one-form Gauss-law can be solved exactly. The physical Hilbert space is parameterized by plaquette electric-flux variables, while the link configuration is reconstructed as the dynamical boundary of the evolving flux domains. The reduced Hamiltonian is an Ising-type plaquette model, where its local transverse-field term is the physical image of the boundary-dressed Wilson operator $\sigma_p^z\prod_{\ell\in\partial p}\tau_\ell^z$. A tube-cap quench compares two initial flux fillings with the same initial boundary loops. Exact diagonalization on $4\times4$, $6\times4$, and $5\times5$ tori finds that the cap loses $20$-$37\%$ of its occupied-flux area, while the tube remains nearly pinned. A finite-size scaling locates a dynamical crossover of tension-to-density ratio near $(m/\varepsilon_E)_c\simeq1.89$. The unreduced plaquette-plus-link encoding provides local Gauss-law checks and a direct digital implementation, while the reduced plaquette-only Hamiltonian supplies the exact benchmark. The result places the specific top-form discharge and the cosmological constant neutralization calculation inside a general higher-form Hamiltonian and coding framework.

We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.

We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. We encode the probabilistic information for the one-particle subsystem in a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from a space-dependence of the mass term in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.

We study chiral symmetry and singlet $U(1)_A$ symmetry in QCD in a background magnetic field using lattice QCD. We first clarify the neutral-sector symmetry structure in a pure magnetic background, where the unequal electric charges of the light quarks explicitly reduce the non-singlet flavor symmetry. We identify the neutral-pion--sigma susceptibility difference, $\chi_{\pi^0}-\chi_\sigma$, as the chiral-partner splitting associated with the surviving neutral non-singlet axial symmetry, and the neutral-pion--delta susceptibility difference, $\chi_{\pi^0}-\chi_{\delta^0}$, as the singlet $U(1)_A$ partner splitting. We also discuss the disconnected contribution to the neutral-pion susceptibility and its continuum constraint. Numerical results are obtained on fixed-scale $(2+1)$-flavor HISQ ensembles with $m_l=m_s^{\rm phys}/10$, corresponding to a pion mass of about $220~{\rm MeV}$ at vanishing magnetic field. We find that the neutral chiral-partner splitting increases with the magnetic field strength $eB$ at low temperature and decreases at sufficiently large $eB$ near the crossover, providing susceptibility-splitting counterparts of magnetic catalysis and inverse magnetic catalysis, respectively. The singlet $U(1)_A$ partner splitting shows an analogous low-temperature enhancement and large-field suppression near the crossover, with the suppression setting in at larger $eB$ and remaining milder than in the chiral channel. These results provide a first lattice-QCD study of neutral-sector probes of chiral and singlet $U(1)_A$ partner susceptibility splittings in background magnetic fields.

We solve the semiclassical Einstein equations for an evaporating Schwarzschild black hole in closed form, obtaining its backreacted geometry in 3+1 dimensions. This is achieved by a reformulation of the Hadamard renormalization prescription, which admits explicit stress-energy tensors for scalar quantum fields in 3+1-dimensional curved spacetimes without the standard mode-sum construction. The Unruh-like states we construct reproduce the Hawking flux at future null infinity and the associated ingoing negative-energy flux at the horizon, yielding the first analytical quasi-stationary solution describing black-hole evaporation in four-dimensional semiclassical gravity. The resulting geometry exhibits a timelike apparent horizon, providing a new analytical setting to study the causal structure of black-hole evaporation and its connection with the information-loss issue. Our results open a new route to semiclassical backreaction in four dimensions, extending the level of analytical control previously available only in two-dimensional effective models.

Analytic infinite derivative gravity theories provide a renormalizable and ghost-free description of gravity around covariantly constant backgrounds. These theories can have non-singular bouncing Universe solutions. In this paper we aim to address a question whether it is possible to realize a bouncing solution without the presence of a ghost or a tachyon instability in this framework. We perform a detailed analysis of degrees of freedom in $(1+3)$ formalism around Minkowski and de Sitter space-times. As a result it becomes clear that on a very general basis one cannot construct an instability free bounce without a negative cosmological constant. An analysis of known bouncing solutions in this model shows that an analyticity of higher derivative form factors in combination with solutions parameters result in the presence of a ghost radiation. Being motivated by the idea of resolving the cosmological singularity problem we proceed by analyzing scalar and tensor modes anyway. Scalar modes appear to not influence Cosmic Microwave Background observations at all, while tensor modes spectrum is computed and the corresponding implications are discussed.

We investigate linear and nonlinear primordial perturbations in an anisotropic Dirac-Born-Infeld (DBI) inflationary model with a non-vacuum initial state. Using the Arnowitt-Deser- Misner (ADM) formalism, we expand the action up to second and third order in the curvature perturbation and derive the corresponding scalar and tensor power spectra, as well as the bispectrum and the equilateral non-linearity parameter \(f_{NL}^{\mathrm{equil}}\). The effects of anisotropic corrections and non-Bunch-Davies (non-BD) initial conditions are incorporated through the slow-roll sector and Bogoliubov coefficients. For the numerical analysis, we consider an intermediate expansion scenario together with a phenomenological ansatz for the excited-state occupation number \(N_k\). By comparing the model predictions with recent observational datasets, including Planck2018 TT, TE, EE + lowE + lensing + BK18 + BAO and DESI+CMB+DESY5 data, we identify observationally viable regions in the parameter space of the model. Our analysis indicates that the anisotropic DBI scenario with non-vacuum initial conditions can remain compatible with current constraints on the scalar spectral index, tensor-to-scalar ratio, and equilateral non-Gaussianity for suitable ranges of the anisotropy parameter \(c\) and the initial-state parameter \(N_{k,0}\).

We analyse the initial-value problem of metric higher-derivative effective theories of gravity. We show that any such theory whose characteristic velocities are independent of derivatives of the metric is intrinsically weakly hyperbolic, independently of the gauge fixing. To show this, we identify the spin-$2$ physical sector directly from the characteristic equation; this can be done without introducing an order-reduced formulation, which greatly simplifies the computation. In this sector, every metric theory with more than two derivatives in the equations of motion contains a weakly hyperbolic block. Since this obstruction is physical, no choice of gauge or constraint addition can remove it, providing a structural explanation for the failure of strong hyperbolicity in this broad class of theories.

The tricritical Ising CFT is the IR fixed-point of $\lambda\phi^6$ theory. It can be seen as a one-parameter family of CFTs connecting between an $\varepsilon$-expansion near the upper critical dimension 3 and the exactly solved minimal model in $d=2$. We review what is known about the tricritical Ising CFT, and study it with the numerical conformal bootstrap for various dimensions. Using a mixed system with three external operators $\{\phi\sim\sigma,\phi^2\sim \epsilon,\phi^3\sim\sigma'\}$, we find three-dimensional "bootstrap islands" in $d=2.75$ and $d=2.5$ dimensions consistent with interpolations between the perturbative estimates and the 2d exact values. In $d=2$ and $d=2.25$ the setup is not strong enough to isolate the theory. This paper also contains a survey of the perturbative spectrum and a review of results from the literature.

We introduce a framework of constrained scalar fields that can give rise to cosmological evolution of the Universe independent of the values of the cosmological constant. Focusing on the simplest realization involving a scalar field with non-minimal coupling, we first study the analytical solutions in the Jordan frame. We show that such solutions include evolution from a radiation dominated-like universe to an exponential expansion, as well as evolution that starts with super-Hubble expansion and then relaxes towards an exponential expansion of the Universe, while describing well-behaved scalar perturbations. We then also relate the theory to the Einstein frame, and analyze the corresponding accelerating solutions. We then consider the model in the presence of external matter. We find that the matter does not affect the evolution of the universe if minimally coupled to the scalar field. In other words, in the Jordan frame, in order to influence the evolution of the space-time, the matter should be non-minimally coupled to the constrained scalar, while it may be minimally coupled to gravity. We show that in this case, the solutions are similar to the free case, and, in addition, allow for the phantom-like equation of state. Finally, we introduce the minimal frame, a frame in which the matter is minimally coupled to both gravity and the constrained scalar, and show that among other possibilities, the phantom-like equation of state can still be realized.

We explore the idea that quantum vacuum energy $\rho_{\rm vac} $ is at the origin of Gravity. We formulate a gravitational version of the electromagnetic Casimir effect, and provide an argument for how gravity can arise from $\rho_{\rm vac} $ by showing how Einstein's field equations emerge in the form of Friedmann's equations. This leads to the idea that Newton's constant $G_N$ is environmental, namely it depends on the total mass-energy of the Universe $M_\infty $ and its size $R_\infty $, with $G_N = c^2 R_\infty /2 M_\infty$. This leads to a new interpretation of the Gibbons-Hawking entropy of de Sitter space, and also the Bekenstein-Hawking entropy for black holes, wherein the quantum information bits are quantized massless particles at the horizon with wavelength $\lambda = 2 \pi R_\infty$. We assume a recently proposed formula for $\rho_{\rm vac} \sim m_z^4/\mathfrak{g}$, where $m_z$ is the mass of the lightest particle, and $\mathfrak{g}$ is a marginally irrelevant coupling. This leads to an effective, induced RG flow for Newton's constant $G_N$ as a function of an energy scale, which indicates that $G_N$ decreases at higher energies until it reaches a Landau pole at a minimal value of the cosmological scale factor $a(t) > a_{\rm min}$, thus avoiding the usual geometric singularity at $a=0$. The solution to the scale factor satisfies an interesting symmetry between the far past and far future due to $a(t) = a(-t + 2 t_{\rm min})$, where $a(t_{\rm min}) = a_{\rm min}$. We propose that this energy scale dependent $G_N$ can explain the Hubble tension and we thereby constrain the coupling constant $\mathfrak{g}$ and its renormalization group parameters. For the $\Lambda{\rm CDM}$ model we estimate $a_{\rm min} \approx e^{-1/\hat{b} }$ where $\hat{b} \approx 0.02$ based on the Hubble tension data.

It is well known that continuous symmetries of quantum fields can be realized non-linearly, e.g. in the context of sigma models, and can also be spontaneously broken on non-compact spacetimes. In this note we study how these effects are realized in the context of the topological symmetry theory for continuous symmetries. In particular, we explain coset realizations and their higher $p$-form symmetry versions from this perspective, as well as uplifts to higher groups and non-invertible symmetries. Moreover, using a setup with boundaries and corners, we explore spontaneous symmetry breaking scenarios for higher $p$-form symmetries as well as non-Abelian $0$-form symmetries.

We show that elliptic curves with complex multiplication (CM) naturally emerge in the spectral geometry of Hermitian one-matrix models in the two-cut phase. Focusing on a symmetric quartic potential, we derive the corresponding genus-one spectral curve and compute its modular $j$-invariant in closed form as a function of the quartic coupling $g$. We identify specific values of $g$ for which the elliptic curve exhibits $CM$, i.e., its endomorphism ring is larger than $\mathbb{Z}$. This establishes a direct connection between number-theoretic structures and the spectral data of random matrix ensembles.

Recently, the generating function has been proposed as an alternative reduction method. This method has been tested at the one-loop level, including the tensor reduction and propagators with higher powers. In this work, we initiate the study of the method for higher loops by focusing on the sunset diagram, which is the simplest nontrivial two-loop integral. By employing PV reduction equations together with syzygy equations, we construct a complete system of differential equations. Through series expansion, we derive a complete set of recurrence relations, which can efficiently reduce any high-rank tensor structure.

In this work, we provide a full map of scattering scenarios between a Nielsen-Olesen vortex and antivortex. Importantly, in the deep type II regime, such a collision reveals a chaotic pattern in the final state formation with bounce windows immersed into annihilation regions. This structure is due to the energy transfer mechanism triggered by a quasinormal mode, specifically the Feshbach resonant mode, hosted by the vortex.

In this work, we investigate the emergence of higher-spin structure in 2d $\mathcal{N}=(0,2)$ disordered models. While previous studies focused on the $J$-type model where the $E$-term in the Fermi multiplet was discarded. We extend the discussion to $\mathcal{N}=(0,2)$ disordered models with $E$-type potential. In terms of (disordered) $\mathcal{N}=(0,2)$ Landau-Ginzburg theory, we establish a duality between two models. By solving the Schwinger-Dyson equations and the ladder kernel matrix for 4-point functions, we verify that the $E$-type model is dynamically equivalent to the $J$-type model in the IR regime. Furthermore, we demonstrate that the $E$-type model also exhibits emergent higher-spin symmetry in certain limits. Our results reveal a larger region of the moduli space of 2D $\mathcal{N}=(0,2)$ disordered theories and provides insights into the holographic transition from finite to tensionless strings that can be diagnosed by the emergence of higher-spin symmetries.

We develop a systematic classification of asymmetric $\mathbb{Z}_2$ orbifold actions in Pati-Salam heterotic string vacua constructed in the free fermionic formulation. Starting from symmetric $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$ orbifold vacua with an $SO(10)$ GUT, we allow the Pati--Salam breaking vector to act asymmetrically on the internal degrees of freedom. The asymmetric orbifold action freezes geometrical moduli whilst inducing doublet--triplet splitting in the untwisted sector. Notably, this doublet-triplet splitting operates for any asymmetric action, including pure asymmetric shifts that preserve all geometric moduli, and is therefore independent of moduli stabilisation. Classifying the breaking vector according to its twist action, we find six inequivalent classes of geometric moduli spaces characterised by 12, 8, 4 or 0 real untwisted moduli. Through combining these asymmetric twists with all compatible asymmetric shifts, 24 inequivalent cases are identified and characterised by their residual moduli content and internal Narain lattice. For each case we construct representative basis sets admitting three chiral generations, providing the starting point for further classification within each class. We perform explicit GGSO (generalized Gliozzi-Scherk-Olive) phase enumerations in representative model classes with 12, 8, 4 and 0 moduli, classify the resulting $\mathcal{N}=1$ and $\mathcal{N}=0$ vacua according to phenomenological criteria and identify exophobic, phenomenologically viable models. We compute the partition function and corresponding one-loop vacuum energy at the free fermionic point in moduli space for each phenomenologically viable model across the four classes. As the number of geometrical moduli decreases, the number of distinct partition functions for these vacua collapses to a small number, reflecting a pronounced degeneracy under GGSO phase variations.

We study a model of 3d gravity relevant to the open sector of a CFT ensemble. The quantum theory is the open Virasoro TQFT, obtained by restricting the full open-closed Virasoro TQFT to a subclass of admissible manifolds. We show that it computes gravitational path integrals on compact regions with fixed-length boundary conditions for states above the black hole threshold, and fixed-angle boundary conditions for states below the threshold. Focusing on a special class of manifolds involving only boundary Wilson loops, we further show that the relation between Conformal Turaev-Viro theory and the diagonal sector of two copies of Virasoro TQFT arises naturally from an open-closed duality.

We determine the type-A Weyl anomaly coefficient $b$, associated with the intrinsic scalar curvature of the defect, for the class of holographically realised co-dimension two defect CFTs (dCFTs) introduced in arXiv: 2506.14505 and arXiv: 2512.14853. At strong coupling, we employ the dual D5-brane solutions in Euclidean signature, where the defect is supported on an $S^2$ submanifold of the Euclidean $AdS_3\times S^1$ boundary. At weak coupling, we use the classical solutions of the ${\cal N}=4$ SYM equations of motion, previously conjectured to describe the defects dual to the D5-brane configurations. Notably, the coefficient $b$ is found to be negative in a finite region of parameter space. To our knowledge, this constitutes the first explicit example of an {\it interacting} unitary dCFT with $b<0$. We also compute the type-B Weyl anomaly coefficients associated with the extrinsic curvature of the defects, first at strong coupling and subsequently at weak coupling. In a certain limit, we find agreement between the weak- and strong-coupling results for both the type-A and type-B anomaly coefficients.

Using the recently developed framework in which cosmological correlators in (E)AdS are represented as flat-space amplitudes dressed by auxiliary propagators, we show that several structural properties of the cosmological observables have a direct flat-space origin. We derive cosmological cutting rules for spinning correlators from the flat-space optical theorem, obtain the cosmological tree theorem from the Feynman tree theorem, and uplift BCFW recursion relations to (E)AdS via dressing. We also show that flat-space soft theorems reproduce the soft limits of (E)AdS correlators, and find indications of an emergent universal structure in subleading soft limits. These results provide evidence that key features of cosmological correlators can be systematically understood as dressed manifestations of flat-space physics.

We present classical magnetic--monopole (MM) and dyon solutions induced by global monopoles in string-inspired gravitational models. Although several ingredients of the construction have appeared previously, we examine a new synthesis via their organised use in a self-gravitating finite-energy monopole/dyon system with explicit mass, charge, core and stability diagnostics. The global monopole provides the topological seed, while the dilaton, Kalb--Ramond (KR) axion and Born--Infeld (BI) electromagnetic (EM) sector supply the string-inspired dressing. Two related branches are analysed: (i) a dilaton--BI magnetic branch, distinct from earlier constructions, and (ii) a dyonic extension in which the KR axion couples electric and magnetic sectors through an axion-Pontryagin-anomaly interaction. In both cases BI dynamics regularises the EM self-energy within a self-gravitating global-monopole construction, and the solutions possess a de Sitter core, a positive ADM-mass parameter range and satisfy the standard energy conditions. A further novel feature is a limiting branch in which the ADM mass tends to zero while the magnetic charge remains finite, the configuration being supported by magnetic charge and de Sitter core this http URL also examine stability diagnostics. The stress--energy tensor gives finite force components and an outward-pointing radial force, indicating absence of core collapse within the mechanical stability criterion. In the exterior analytic region we analyse gauge-invariant EM perturbations using the Gervalle-Volkov framework. The helicity modes $\psi_\pm$ obey a self-adjoint Sturm--Liouville system. MM helicities decouple, while dyons exhibit axion-induced helicity mixing and birefringent polarisation structure. Positivity of the EM helicity block provides a necessary long-range stability diagnostic; the full coupled Einstein-matter spectral problem is discussed

We study the dynamics of first-order inverse phase transitions (driven by superheating) at strong coupling, focusing on the top-down Witten-Sakai-Sugimoto model for holographic QCD. Two cases are considered: the deconfinement transition in the unflavored version of the model and a chiral symmetry-restoring transition occurring in the deconfined phase of the full theory. In both cases, we imagine driving the system into a metastable phase at high temperature, inducing the nucleation of bubbles of the stable phase. For both classes of transitions, we find the corresponding Euclidean bounce solutions and compute the bubble nucleation rates and the relevant transition parameters. For the deconfinement transition, the large jump in the number of degrees of freedom between the two phases suggests that the bubble wall velocity is parametrically small; we provide a rough estimate of it near the critical temperature. In the case of the chiral transition, instead, we compute the bubble wall velocity and the friction force exerted on the bubbles employing motivated ansatze and approximations for the steady-state configurations.

The holographic time-like entanglement entropy (TEE) extends entanglement to time-like boundary subregions. While its definitive holographic dictionary remains debated, one concrete proposal utilizes piece-wise extremal surfaces. In this work, we adopt this geometric prescription as an exploratory framework to holographically investigate the late-time ($\tau_0\to \infty$) growth of TEE in asymptotically AdS black holes with a space-like singularity and no inner horizon. By assuming a Kasner geometry near the space-like singularity and using the null energy condition, we analytically show that a critical extremal surface $\mathcal{A}_c$ inside the event horizon completely governs the late-time linear growth of the TEE. This result suggests that the late-time behavior of TEE is tightly constrained by the geometry of black hole interiors. While the dominant energy condition (DEC) guarantees an upper bound for the real part's growth rate, we conjecture a corresponding universal lower bound for the imaginary part. Numerical results from Einstein-scalar theory demonstrate the robustness of this bounding behavior: the vacuum Schwarzschild-AdS geometry consistently maximizes the real growth rate and minimizes the imaginary part, suggesting these bounds hold in broader holographic setups.

We study tree-level Yang--Mills wavefunctions in four-dimensional de Sitter space using their discontinuities. Cosmological cuts factorize gluon discontinuities into lower-point wavefunctions glued by cut propagators and transverse projectors. For ray-like trees and one-loop $n$-gons, the maximal cuts take a particularly simple form: a scalar $\phi^3$ discontinuity dressed by an ordered Yang--Mills numerator built from local gluing maps. We then use these cuts as reconstruction data for the four-, five-, and six-gluon wavefunctions in momentum space. The result separates into a cut-detectable part obtained from lower-point gluing and a cut-invisible completion fixed by current conservation and the flat-space limit. Through six points, the terms without longitudinal propagators follow the pole structure of color-ordered scalar $\phi^3+\phi^4$ wavefunctions, dressed by local Yang--Mills numerators. Longitudinal propagators collapse part of this scalar structure into contact-type contributions, with the first internal-line corrections appearing at six points. The reconstructed expressions agree with direct momentum-space Feynman-rule computations and give concrete low-point data for an all-$n$ organization of spinning de Sitter wavefunctions.

We present new charged and rotating near-horizon geometries in five-dimensional Einstein-Maxwell theory in closed analytic form. The solutions can be parametrised by the charge and two independent angular momenta. We also generalise these near-horizon geometries to theories with an additional Chern-Simons term in the action multiplied by an arbitrary coupling constant. The new solutions have the same entropy relations as expected for charged versions of extremal Myers-Perry black holes and for rotating versions of extremal Reissner-Nordström-Tangherlini black holes, but they do not reduce to the Myers-Perry horizon in the vacuum limit. The horizon cross-sections are spherical and carry a Sasakian structure. We exploit this structure to prove a characterisation of our solutions: without any symmetry assumptions, they are the most general rotating extremal horizons for which the co-rotating electric field is a (non-zero) constant. We further extend this construction to higher dimensions, where we show that any Sasaki-Einstein manifold generates a two-parameter family of charged and rotating horizons.

We generalize the "holar wind" mechanism proposed in arXiv:2303.00234 to the case of rotating $\lambda$-deformed BTZ black holes. These backgrounds, which interpolate between $AdS_3$ in the infrared and a linear dilaton spacetime in the ultraviolet, are realized as an exact $\frac{SL(2,\mathbb{R})_k\times U(1)}{U(1)}$ gauged-WZW worldsheet theory. The long string sector of the theory provides a holographic dual to single-trace $T\overline{T}$ deformed symmetric product $\mathcal{M}^p/S_p$ $CFT_2$ with a seed $\mathcal{M}$ carrying a central charge $c=6k$. By analyzing the geodesics and tunneling rates of probe particles and winding long strings, we show that the emission probabilities for both positive and negative deformation couplings are universally governed by the change in the Bekenstein-Hawking entropy, $\Delta S_{BH}$. A central result of our analysis is that the consistency of long string emission within the grand canonical ensemble dictates a unique value for the background B-field at the origin. We demonstrate that this thermodynamically fixed value matches precisely the prediction required for the string excitation spectrum to agree with the $\mathbb{Z}_w$ twisted sector of a single-trace $T\overline{T}$ deformed symmetric product orbifold. Finally, we sketch the extension of these results to a broader class of black holes whose long string sector is dual to single-trace $T\overline{T} + J\overline{T} + T\overline{J}$ deformed theories.

We point out that the masses of the highly excited bound quark-antiquark states in QCD$_2$ in the infinite $N$ limit may be determined in the framework of a simple quantum-mechanical model with the potential $V(x) = \sigma |x|$. In the ultrarelativistic case, the masses follow the pattern $$ \mu_n^2 \ =\ \frac {g^2 N}{2\pi} n, $$ which coincides with the law derived by `t Hooft by solving the Bethe--Salpeter equation. In the nonrelativistic case, the energy levels follow the asymptotics $\epsilon_n = \mu_n - 2m = Cn^{2/3}$, where the constant $C$ can be determined by solving the `t Hooft equation or alternatively the nonrelativistic Schrödinger equation.

In Yang-Mills theory on a Euclidean Cauchy surface, the physical gauge group is often taken to be $\mathcal{G}^I/\mathcal{G}^\infty_0$, where $\mathcal{G}^I$ consists of boundary-preserving gauge transformations asymptoting to a constant, and $\mathcal{G}^\infty_0$ consists of transformations generated by the Gauss law constraint. We rigorously derive this physical gauge group for both Abelian and non-Abelian theories. A key result is that restricting to $\mathcal{G}^I$ follows from the structure of the instantaneous state space on which the instantaneous Lagrangian is defined. We extend our analysis to Yang-Mills-Higgs theory, showing that boundary conditions and the physical gauge group differ between the unbroken and broken phases.

We investigate particle production by a pseudo-Nambu-Goldstone boson (pNGB) in the spontaneous baryogenesis scenario for large misalignment angles. Since the fermionic backreaction is intrinsically nonlocal, the large-angle problem is in general difficult to treat directly. We argue that the adiabaticity conditions are parametrically satisfied in the model, allowing the backreaction to be described by a local Markovian approximation while retaining the nonlinear dependence of the pNGB potential on the angular field. Through a numerical study of arbitrary initial phases, we reproduce the cubic dependence of the baryon asymmetry for small oscillations and demonstrate that this behavior breaks down for large oscillations, especially for initial phases close to $\pi$. Our calculations indicate that particle production saturates as the initial phase approaches $\pi$ in Minkowski spacetime. Furthermore, numerical solutions are presented in conformal Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. These solutions show a strong dependence of baryon excess generation on the damping rate of the pNGB field oscillations. We also discuss the probability distribution of the baryon asymmetry.

We revisit Coincident General Relativity (CGR) in the gauge approach to gravity based on Symmetric Teleparallel Equivalent to General Relativity (STEGR) in the \textit{internal-space formulation}, which one of the authors recently proposed in Ref.~[J. Math. Phys. 66 (2025) 5, 052505]. First, we review the standard formulation of STEGR theories in the Palatini approach to gravity, in which formulation we impose the teleparallel and torsion-free conditions by using Lagrange multipliers. Second, we introduce the STEGR theories in the gauge approach to gravity, which is formulated in the internal space, and derive its field equations. We briefly discuss whether the Ostrogradski ghost instability exists and find that the theory may require a degenerate condition to be imposed. Finally, assuming the coincident gauge, we derive CGR in both terms of the action integral and the field equation. Discussing the possible kinematics of the STEGR theory, we formulate a motion of a test scalar particle in the spacetime with non-metricity.

We investigate the thermodynamic phase structure of a nonminimally coupled magnetic AdS black hole through the dynamics of timelike particles. The free energy analysis reveals a Van der Waalslike phase transition characterized by small, intermediate, and large black hole phases. We show that both the Lyapunov exponent of unstable circular orbits and the quasi-periodic oscillation (QPO) frequencies associated with stable circular orbits exhibit clear signatures of underlying thermodynamic phase structure, including first order and critical phase transitions. More importantly, we establish a QPO-Lyapunov exponent mapping and demonstrate that the resulting relation inherits the same thermodynamic branch structure. Although the Lyapunov exponent and QPO frequencies originate from unstable and stable circular orbits, respectively, their correspondence emerges from the common black hole spacetime geometry and remains valid even in the absence of phase transitions. Our results reveal an unexplored connection among orbital instability, QPO phenomenology, and black hole thermodynamics, suggesting a potential observational route for probing chaotic orbital dynamics and thermodynamic phases through QPO measurements.

High-energy QCD evolution beyond leading order suffers from instabilities driven by large collinear logarithms. We present a framework, consistent with the standard high-energy operator product expansion (OPE), that restores perturbative stability order by order. The method involves a change of basis in the space of high-energy operators, which modifies both the evolution kernel and the coefficient functions while leaving physical observables invariant. Within this factorization scheme, we derive a next-to-leading-order renormalization-group equation whose numerical solution exhibits stable evolution up to large rapidities, paving the way for a systematic framework for precision studies of gluon saturation at current and future colliders.

In this work, we investigate the behaviour of the periapsis shift in static charged black-hole spacetimes, focusing on the interplay between extremality and the Aschenbach-like effect. We first examine the evolution of orbital dynamics as the extremal limit is approached in representative charged black-hole models. We then extend the analysis to black-hole geometries that admit a stable photon sphere outside the event horizon, where the Aschenbach-like effect has previously been identified. Our results show that the periapsis shift remains a well-defined dynamical quantity in the extremal regime and continuously reflects changes in the underlying spacetime geometry. For black-hole solutions possessing an external stable photon sphere, the associated minimum of the effective potential produces characteristic modifications in both the angular-velocity profile and the periapsis shift. When extremality and the Aschenbach-like effect coexist, the orbital dynamics undergo a qualitative transition, giving rise to a three-region structure consisting of an inner prograde region, an intermediate retrograde region, and an outer prograde region. Within the black-hole models investigated in this work, such behaviour is absent from the other configurations considered. These results demonstrate that the periapsis shift provides a sensitive dynamical probe of strong-field black-hole spacetimes, encoding both geometric and orbital information beyond that obtained from photon-sphere analyses alone. Our findings highlight the rich orbital structure that can emerge from the combined presence of extremality and an external stable photon sphere and provide a useful framework for future studies of orbital dynamics in modified theories of gravity.

In the single-field case, Horndeski provides the most general scalar-tensor theory with second-order field equations. By contrast, systematic multi-field extensions remain incomplete: while the general field equations for the bi-Horndeski case are known, a general action has not been established, and for cases with three or more fields, neither a general action nor general equations are available. We characterize Horndeski theory by three mild axioms: closure under invertible pure disformal transformations, the inclusion of a minimal Horndeski theory as an anchor, and the requirement that the coefficient functions of the Lagrangian be arbitrary up to relations required by the closure. Under this characterization, we recover the standard single-field action up to boundary terms and obtain a practical path to multi-field constructions. In particular, we show that antisymmetric structures, such as those identified by E. Allys, S. Akama, and T. Kobayashi, appear within this framework, and indicate that this viewpoint has the potential to account for features captured by known bi-Horndeski equations.

The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. Here, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework connecting both limiting cases, and is intended as a bridge between advanced quantum mechanics and field-theoretic treatments of dispersion forces, suitable for graduate-level courses or specialized readers.

We study Oppenheimer-Snyder (OS) gravitational collapse matched to a general static, spherically symmetric exterior spacetime. Unlike the Schwarzschild case, two new features can arise in black holes with two horizons: an apparent-horizon minimum, a temporary minimum in the apparent-horizon radius during collapse, and a bounce, where the star surface stops collapsing at a nonzero radius and reverses into expansion. We identify the conditions that lead to these two features. For two-horizon exteriors, trapped-region consistency requires that the apparent-horizon turning point occurs no earlier than the surface crossing of the inner horizon. As a concrete example, the OS collapse of the Reissner-Nordström (RN) spacetime shows both effects. In contrast, regular black holes with de Sitter cores show neither: their collapse is smooth and monotonic, and the surface approaches the center only as the proper time goes to infinity. These results naturally classify the OS collapses into three categories: singular, which ends at the center in finite time; bouncing, which reverses at a finite radius; and soft-landing, which reaches the center only asymptotically. We argue that these features are consistent with Penrose's strong cosmic censorship conjecture.

We investigate operator growth in a Brownian spin Sachdev--Ye--Kitaev (SYK) model with random all-to-all interactions, focusing on the full operator-size distribution. For Hamiltonians containing interactions of order two up to $L$, we derive a closed master equation for the Pauli-string expansion coefficients and recast their dynamics into a generating-function formulation suitable for the large-$N$ limit. This approach allows us to diagonalize the leading-order evolution operator explicitly and obtain exact solutions for arbitrary initial operator distributions, including the effects of decoherence. Going beyond leading order, we develop a systematic $1/N$ expansion that captures higher-order corrections to the operator-size dynamics and the late-time behavior. Our results demonstrate that higher-order effects play a crucial role in operator scrambling and that the full operator-size distribution provides a more refined probe of quantum chaos in Brownian and open quantum systems.

We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $\Psi$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $\langle \Psi^2 \rangle_{\textrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $\eta$ and retaining terms through $O(\eta^2)$, we find that $\langle \Psi^2 \rangle_{\textrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result - with the event horizon radius modified by the presence of $\eta$. We also investigate whether an analogous decomposition holds for $\langle T^{\mu}_{\phantom{\mu}\mu}\rangle_\textrm{ren}$ when it is determined by. Our result parallels earlier analyses of Schwarzschild black holes pierced by a cosmic string.

We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms organized in inverse powers of the ultraviolet energy cut-off $E_{\rm max}$. Building on the leading-order matching program, we develop two complementary extensions. First, we derive compact all-order expressions for the local matching corrections to the mass and quartic coupling by resumming infinite classes of diagrams sharing fixed topologies within the local approximation. Second, we extend the non-local sector by computing the next-to-next-to-local corrections contributing at $\mathcal{O}(E_{\rm max}^{-4})$, following a continuum-first matching procedure, in which the effective corrections are computed in infinite volume and the spatial direction is subsequently re-compactified to obtain a discrete basis of free-Hamiltonian eigenstates on which the truncated operator construction is implemented. Our results show that an increasingly rich operator basis is necessary to describe the theory beyond leading order.

We show that the Lagrangian of a Nambu-Goto $p$-brane satisfies the identity $\mathcal{L}_{\rm [\it p \rm]}=T_{\rm [\it p \rm]}/(p+1)$, with $T_{\rm [\it p \rm]}$ denoting the trace of the corresponding energy-momentum tensor, independently of the properties of the gravitational field. While for $p=0$ this reduces to the standard $\mathcal{L}_{\rm [0]}=T_{\rm [0]}$ relation, which determines the on-shell Lagrangian of point particles and their fluids, more generally it depends explicitly on the $p$-brane dimensionality. We explore the implications of this Lagrangian identity for the dynamics of non-self-intersecting cosmic string loops in a homogeneous and isotropic universe within nonminimally coupled scalar-tensor gravity, showing that, unlike in general relativity, their rest mass can evolve in response to the cosmological evolution of the background spacetime, regardless of their small size or tension. We further generalize this analysis to closed $p$-branes in $(N+1)$-dimensional Friedmann-Lemaître-Robertson-Walker spacetimes, showing that the evolution of the rest mass depends explicitly on the dimensionality of the brane, and therefore that the cosmological evolution of particle-like objects in theories of gravity with nonminimal matter couplings is sensitive to their internal structure.

Non-linear interactions during inflation generate non-Gaussianities in the distribution of primordial curvature. In many theories, the physics is scale-invariant, such that the induced three-point function depends solely on a dimensionless shape function $S(x,y)\sim k^6B_\zeta(kx,ky,k)$. To confront such models with observations, one typically builds specialized estimators for each shape, then applies them to cosmic microwave background datasets at significant computational expense. In this Letter, we take a different approach, directly reconstructing $S(x,y)$ from observations using an efficient logarithmically-binned estimator in primordial-space (motivated by the modal program). Applying this to temperature and polarization maps from Planck, we obtain high-resolution shape measurements across the full $(x,y)$-plane, including squeezed limits. Our approach is close-to-optimal, highly interpretable, and preserves the information content on (optimally-analyzed) standard templates within $\approx 10\%$; moreover, we can use it to assess the scale-dependence of our constraints, finding that Planck is sensitive to $\approx 6$ $e$-folds of non-Gaussian evolution with a peak sensitivity around $0.1h\,\mathrm{Mpc}^{-1}$. Since we work directly in shape-space, data and theory can be compared in milliseconds. As an example, we perform a search for massive particle exchange using a suite of over $20\,000$ theoretical templates computed with exact bootstrap methods across a wide range of masses, spins, and sound-speeds; the spin-two analysis yields a maximum significance of $2.6\sigma$. Our approach can be used to probe a wide range of scale-invariant models in orders-of-magnitude less time than with direct estimators, facilitating new exploration of the inflationary paradigm.

We study quantum and stochastic deformations of the rule-54 reversible cellular automaton (RCA54) on a 1+1-dimensional spatiotemporal lattice, focusing on their integrability structures in two distinct settings. First, for the quantum deformation, which turns the model into an interaction-round-a-face brickwork quantum circuit (either on an infinite lattice or with periodic boundary conditions), we show that the shortest-range nontrivial conserved charge commuting with the discrete-time evolution operator has a density supported on six consecutive sites. By constructing the corresponding range-6 Lax operator, we prove that this charge belongs to an infinite tower of mutually commuting conserved charges generated by higher-order logarithmic derivatives of the transfer matrix. With the aid of an intertwining operator, we further prove that the transfer matrix commutes with the discrete-time evolution operator. Second, for the stochastic deformation, which renders the model into a Markov-chain circuit, we investigate open boundary conditions that couple the system at its edges to stochastic reservoirs. In this setting, we explicitly construct the non-equilibrium steady state (NESS) by means of a staggered patch matrix ansatz, a hybrid construction combining the previously used commutative patch-state ansatz for the undeformed RCA54 with the matrix-product ansatz. Finally, we propose a simple empirical criterion for detecting integrability or exact solvability in a given model setup, introducing the notion of digit complexity.

In this work, we investigate the structure of black hole shadows in the bumblebee gravity model formulated within the metric-affine framework, which incorporates spontaneous Lorentz symmetry breaking (LSB) through a vector field $B_\mu$ with a non-zero vacuum expectation value. We analyze the influence of the dimensionless rotation parameter $a = J/M$ and the Lorentz-violating (LV) coefficient $X = \xi b^2$ on the photon sphere radius, the critical impact parameter, and the shadow morphology. Using ray-tracing simulations with the GYOTO code and accretion disks, we observe that increasing values of $X$ induce progressive vertical flattening, asymmetric ``teardrop''-shaped deformations, and local collapse of the lower silhouette region, interacting with the rotational Doppler effect. These anisotropic signatures distinguish the bumblebee model from the standard Kerr metric and provide observational tests for LSB effects in strong gravity regimes, potentially detectable by the Event Horizon Telescope in sources such as M87* and Sgr A*.

In this work, we propose a novel experimental set-up using charged resonant gravitational wave detectors. We exploit the semi-classical analogue of the Gertsenshtein effect where the gravitational wave acts as an modulator for the optomechanical system. We consider a cavity QED scenario where the Weber bar is placed inside an electromagnetically shielded cavity. We observer that when the gravitational wave falls on the Weber bar, it emits photon which signifies the detection of gravitational waves by the resonant bars. The frequency controlled spontaneous emission scenario will shed a new light on future generation of efficient gravitational wave detector models.

We introduce the \emph{flavoured lattice Schwinger model}, a $(1{+}1)$-dimensional $U(1)$ lattice gauge theory in which the fermion doubling problem is resolved by staggering a $\mathbb{Z}_{2}$ flavour degree of freedom rather than staggering chirality. Unlike the standard approaches, this construction preserves an exact axial $U(1)$ symmetry at finite lattice spacing. We derive the continuum limit, showing that the model reduces to the \emph{two-flavour} massless Schwinger model, with flavours $\alpha\in\{0,1\}$ sharing one dynamical $U(1)$ gauge field. The central result is a well-defined, regularised, gauge-invariant lattice axial charge $Q_{G}^{A}$ whose continuum non-conservation $\langle dQ_{G}^{A}/dt\rangle = -(2g/\pi)\!\int\! dx\,\langle E(x)\rangle$ arises as a direct dynamical consequence of minimal gauge coupling. A particle-hole transformation on the $\chi$ flavour exposes a hidden $U_{L}(2)\times U_{R}(2)$ chiral symmetry; non-Abelian bosonisation then identifies the model with a massive abelian Schwinger sector tensored with the level-$1$ $SU(2)$ Wess--Zumino--Witten model. Finally, we show that embedding the flavoured fermions in a ribbon-shaped $(2{+}1)$D Bernevig--Hughes--Zhang topological insulator and gauging the bulk in a constant background field factorises the boundary theory into \emph{two decoupled} single-flavour Schwinger models, one on each edge, identifying the lattice factor of $2$ as one quantum of Schwinger anomaly per edge.

We investigate the Raychaudhuri dynamics of charged spin-nondegenerate Lorentz-violating particle congruences under minimal electromagnetic coupling. The coupling is introduced through the gauge-covariant momentum $P_{\mu}=\pi_{\mu}-qA_{\mu}$, so that the branch dispersion relation keeps its free functional form, while the electromagnetic field enters through the evolution of $P_{\mu}$. For a generic branch $\mathcal D^{(\pm)}(P)$, the tangent $k^{\mu}_{(\pm)}$ and the momentum Hessian $M^{\mu\nu}_{(\pm)}$ determine the covariant acceleration, $a^{\mu}_{(\pm)}=-qM^{\mu\nu}_{(\pm)}F_{\nu\rho}k^{\rho}_{(\pm)}$. As a consequence, the Raychaudhuri equation acquires the branch-dependent electromagnetic source $-q\nabla_{\mu}\!\left(M^{\mu\nu}_{(\pm)}F_{\nu\rho}k^{\rho}_{(\pm)}\right)$. We apply this construction to the $b_{\mu}$, $H_{\mu\nu}$, and $d_{\mu\nu}$ sectors, obtaining the corresponding branch tangents, Hessians, accelerations, and focusing equations. In flat spacetime, the electromagnetic field modifies the expansion through the divergence of the effective branch force. Therefore, uniform fields may bend the trajectories, whereas local focusing requires field gradients or, in the magnetic case, a coupling to an already deformed congruence. We also develop the analogous description for semiclassical quasiparticle beams, where the band Hessian plays the role of an effective electromagnetic response tensor. For anisotropic parabolic, Dirac-like, and Weyl-type dispersions, the same geometric structure relates electromagnetic textures to beam focusing. In two-branch systems, the opposite Hessians of the branches can produce focusing in one congruence and defocusing in the other, giving a quasiparticle realization of branch-dependent birefringence.

In this paper, we presented an approximate analytical treatment of the Coulomb plus logarithmic potential using perturbation theory to investigate the mass spectra of bottomonium and charmonium mesons for the low-order quantum states. The derived energy equation, to first-order corrections, was employed to model the free potential parameters through fitting to experimental data of the Particle Data Group. The proposed potential successfully reproduces asymptotic freedom at short distances through one-gluon exchange interactions and quark confinement at large distances, which are the essential features of the strong interactions in Quantum chromodynamics theory. The calculated bottomonium masses exhibited excellent agreement with experimental values, yielding an absolute percentage average deviation (APAD) of 0.24%, which improves upon several previously reported theoretical results. Similarly, the vector and pseudoscalar charmonium masses were obtained with an APAD of 1.65%, demonstrating improved and comparable accuracy relative to existing competing theoretical calculations. Although our results were limited to first-order corrections to the energy spectra within the perturbation theory, the reliability of the approximation was validated by comparison with exact numerical solutions obtained using the matrix Numerov method. The small percentage errors obtained confirm the effectiveness of the phenomenological potential and perturbation approximation in describing quarkonia systems. The results suggest that the approach can be reliably extended to higher excited states.

We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner$-$Sharp quasilocal mass and the Wald Noether$-$charge entropy in scalar$-$tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, we derive explicit Einstein-frame scalar potentials: for Barrow entropy, a steep exponential potential; for Tsallis$-$Cirto entropy, an exponential potential governed by the nonextensivity parameter; and for quantum-gravity and entanglement$-$induced corrections, an approximately linear potential. These distinct potentials generate characteristic cosmological phenomenology, with implications for inflationary dynamics, late-time dark-energy behavior, and non-singular bouncing cosmologies. The framework is compatible with current constraints from solar-system tests, big-bang nucleosynthesis, and pulsar-timing observations, and it yields predictions that can be probed by forthcoming observational surveys. In this way, the analysis establishes a unified and geometrically grounded connection between information$-$theoretic entropy proposals and gravitational field theory.

We investigate static, spherically symmetric (SS) spacetimes in covariant teleparallel \(F(T)\) gravity in the presence of electromagnetic sources. Starting from the coframe/spin-connection (CSC) pair formalism, we derive the field equations and associated conservation laws, which constrain admissible electromagnetic configurations and reconstructed teleparallel sectors. A general reconstruction procedure is established, allowing the systematic construction of nonlinear teleparallel \(F(T)\) models for arbitrary coframe ansätze. Focusing on power-law (PL) configurations, we obtain several classes of exact solutions, including constant-radius, black-hole-like (BH-like), and wormhole-like (WH-like) branches, and analyze their horizon structures, torsion singularities, and stability properties. The inclusion of electromagnetic sources leads to new charged solutions that generalize Reissner--Nordström (RN) spacetimes and reveal modified near-horizon and asymptotic behaviors. The results are further organized within an invariant classification framework, highlighting the role of torsion in shaping the solution space. Overall, this work provides a unified and covariant approach to the construction and interpretation of physically relevant compact-object, effective cosmological, and regularized strong-field sectors in nonlinear teleparallel gravity, with potential implications for strong-field tests beyond General Relativity (GR).

A covariant reconstruction framework for electromagnetic Kantowski--Sachs (KS) geometries in teleparallel $F(T)$ gravity is developed using the coframe/spin-connection (CSC) formalism and the invariant approach. In a restricted Maxwell-compatible branch, the electromagnetic conservation laws strongly constrain the anisotropic KS scale factors and lead to the scaling $\rho_{\mathrm{em}}\propto A_3^{-4}$. The corresponding symmetric and antisymmetric field equations are derived and used to reconstruct the functional form of $F(T)$ directly from the KS dynamics. Power-law and exponential ansätze generate distinct invariant reconstruction branches associated with electric, magnetic, and transverse electromagnetic sectors. The exponential branch naturally admits reduced teleparallel de Sitter limits and shifted models of the form $F(T)=f(T_0-T)$. The reconstructed branches describe anisotropic cosmological sectors together with local BH-interior-like sectors that may reproduce reduced BH-interior-like or RN--dS-type behaviors at the level of the KS dynamics. These branches are organized through the invariant coframe/spin-connection classification and screened using the necessary leading-order viability conditions $F_T>0$ and $F_{TT}>0$. The local and branch-dependent nature of the construction is emphasized throughout.

The Haldane-Shastry spin chain is a prototypical integrable model with long-range interactions, notable for hosting quasiparticles with fractional statistics and serving as a discrete analogue of a conformal field theory. Its remarkable simplicity is closely tied to a full Yangian spin symmetry. While the highest-weight states for this symmetry are known explicitly, a systematic treatment of the descendant states, needed for the computation of various physical quantities, has remained incomplete. In this work, we provide a detailed construction of these descendants in terms of the algebraic Bethe ansatz following recent work of Ferrando et al. In the limit of extreme twist, it includes the Gelfand-Tsetlin basis. As an application, we derive product and determinant formulae for norms and overlaps of these states.

Existence of Double-Logarithmic (DL) contributions to scattering amplitudes in QED was discovered by V.V. Sudakov in 1956 and total summation of DL contributions to electron-photon scattering resulted in appearance of famous Sudakov exponentials. Then, thanks to contributions of V.G. Gorshkov, V.N. Gribov, G.V. Frolov and L.N. Lipatov, the pattern of calculations in Double- Logarithmic Approximation (DLA) was constructed. Since then, DLA has become one of basic ways of describing various high-energy processes in the framework of QED, QCD and theory of EW interactions. In the present paper, we remind the history of DLA and present a brief overview of application of DLA to various objects like form factors, scattering amplitudes, DIS structure functions.

Supermassive black holes (SMBHs) powering quasars at $z \gtrsim 6$ are difficult to grow from stellar mass remnants, motivating seeds from primordial black holes (PBHs) with masses $10^5-10^7 M_{\odot}$. This range is constrained by the COBE/FIRAS bound on the CMB $\mu$-distortion, which limits the small-scale curvature variance to $\sigma_\zeta^2 \lesssim 10^{-4}$. For Gaussian perturbations, the variance fixes the far tail of the one-point probability distribution function (PDF), making the PBH abundance negligible. We call this the Gaussian barrier. The barrier can be evaded only if the variance probed by the distortion is decoupled from the tail probability controlling collapse. We implement this idea in the non-perturbative $\delta N$ formalism and relate asymptotic PDF tails to the global shape of the $\delta N$ map. Four Gaussian-cored families are analyzed: generalized-normal, stretched-exponential, power-law, and log-normal tails. After standardizing each family to unit variance, we impose the FIRAS cap and compute the distortion-limited PBH abundance in the tail-shape parameter space. The ordinary exponential tail produced by standard single-field non-attractor dynamics is still too light to reopen the seed window. Algebraic tails from fractional-potential dynamics, and sufficiently heavy log-normal tails treated as a phenomenological proxy for multiplicative dynamics, can supply seed-relevant abundances while respecting the distortion bound.

Regular black holes in Horndeski theories must have stable horizons and regular centers. We study static, spherically symmetric, asymptotically flat configurations with a time-independent scalar. The horizon branch on which the scalar kinetic term $X$ remains nonzero is generically obstructed by divergent propagation speeds or ghost/gradient instabilities, aside from special degeneracies. On the regular branch, where $X$ vanishes at the horizon, analyticity at the relevant $X=0$ endpoints reduces the leading scalar equation to finite sets of Taylor coefficients. For nondegenerate shift-symmetric theories this gives a nonperturbative current no-hair theorem: the scalar is constant and the metric is Schwarzschild, hence centrally singular for nonzero ADM mass. For non-shift-symmetric positive-power couplings, the corresponding exclusion applies to the perturbative branch continuously connected to Schwarzschild. We also classify marginal nonanalytic departures: covariant regularity fixes the scalar-Gauss-Bonnet chain as the unique marginal nonanalytic completion. Hairy black holes in this completion evade the analytic current step but remain centrally singular.