Mass formulas evaluate the total weighted count of a given class of algebraic structures, such as lattices or codes. We show that 3d TQFTs provide a generalization of this concept: the total weighted count of topological boundary conditions is given by the TQFT partition function averaged over all closed 3d manifolds. This weighted count, which we call the mass, can be interpreted as the renormalized partition function of TQFT gravity. For Abelian TQFTs, the mass formula for topological boundary conditions reduces to the mass formula for particular families of codes. Focusing on the Abelian case, we show how to evaluate the mass for any bosonic theory and consider many explicit examples. We then discuss the non-Abelian generalization and compute the mass for $n + \bar n$ copies of the Ising modular tensor category. Finally, we generalize the construction to five dimensions and compute the mass for Abelian 2-form Chern-Simons theories.

The Dirac-Bergmann algorithm for the Hamiltonian analysis of constrained systems is a nice and powerful tool, widely used for quantization and non-perturbative counting of degrees of freedom. However, certain aspects of its application to systems with first-class constraints are often overlooked in the literature, which is unfortunate, as a naive treatment leads to incorrect results. In particular, when transitioning from the total to the extended Hamiltonian, the physical information encoded in the constrained modes is lost unless a suitable redefinition of gauge invariant quantities is made. An example of this is electrodynamics, in which the electric field gets an additional contribution to its longitudinal component in the form of the gradient of an arbitrary Lagrange multiplier. Moreover, Dirac's conjecture, the common claim that all first-class constraints are independent generators of gauge transformations, is somewhat misleading in the standard notion of gauge symmetry used in field theories. At the level of the total Hamiltonian, the true gauge generator is a specific combination of primary and secondary first-class constraints; in general, Dirac's conjecture holds only in the case of the extended Hamiltonian. The aim of the paper is primarily pedagogical. We review these issues, providing examples and general arguments. Also, we show that the aforementioned redefinition of gauge invariants within the extended Hamiltonian approach is equivalent to a form of the Stueckelberg trick applied to variables that are second-class with respect to the primary constraints.

Loops of virtual particles from the vacuum of quantum field theory (QFT) render black holes tidally deformable. We compute the static tidal response of unspinning charged black holes at arbitrary radius, using the perturbative formalism developed in 2501.18684. Since the gravitational and electromagnetic tidal responses mix, we generalize the notion of Love numbers to Love matrices. We derive the coupled equations of motion for the metric and electromagnetic fluctuations around purely electric and magnetic backgrounds. For large charged black holes, which are described by the Effective Field Theory (EFT) of gravity, we compute the full set of Love matrices induced by an arbitrary tower of $F^{2n}$ operators. We find that, although quantum corrections break electromagnetic duality, the Love matrices in electric and magnetic backgrounds are related by a $Z_2$ symmetry under electric-magnetic exchange. Going beyond EFT, we compute the Love matrices of small magnetic black holes. We show that the running of the Love matrices is governed by the running of the $U(1)$ gauge coupling, and we derive the correspondence between Love and $U(1)$ beta functions for arbitrary harmonics. The overall picture that emerges is that the QFT-induced tidal response of magnetic black holes saturates in the strong-field regime. These results imply that nearly-extremal magnetic black holes charged under an Abelian dark sector could be probed by gravitational-wave observations.

We embed the covariant, gauge-invariant gravitational radiation criteria of Fernández-Álvarez and Senovilla, based in terms of conformal geometry and the Bel-Robinson tensor, into the hydrodynamic framework of gauge/gravity duality. This construction uncovers a direct correspondence between bulk gravitational waves and dissipative processes in the boundary theory, from which a natural notion of entropy production emerges. We further analyze a smooth flat limit in which the dual fluid becomes Carrollian, with dissipation governed by Carroll-covariant tensors. As an example, we apply our framework to the Robinson-Trautman family of solutions.

We propose a new class of sigma models based on Courant sigma models. We refer to these models as gauged Courant sigma models (GCSMs). By introducing additional gauge symmetries, such as those associated with a Lie group, a Lie groupoid (or Lie algebroid), and a Courant algebroid on the target space, Courant sigma models are extended to gauged sigma models of AKSZ type. The consistency of the theory is ensured by identities among geometric quantities on Lie algebroids and Courant algebroids, such as curvatures and torsions, which can be interpreted as flatness conditions on the target space. We also analyze geometric structures of GCSMs in the presence of fluxes and boundaries.

We advance ``Latent entropy" (L-entropy) as a novel measure to characterize genuine multipartite entanglement in pure states, applicable to quantum systems with both finite and infinite degrees of freedom. This measure, derived from an upper bound on reflected entropy, attains its maximum for three-party GHZ states and $n=4,5$-party $2$-uniform states. We establish that it satisfies all essential properties of a genuine multipartite entanglement measure, including being a pure-state entanglement monotone. We further obtain an analogue of the Page curve by analyzing the behavior of L-entropy in multiboundary wormholes, emphasizing their connection to multipartite entanglement in random states. Specifically, for $n = 5$, we show that random states approximate $2$-uniform states, exhibiting maximal multipartite entanglement. Extending these ideas to finite temperatures, we introduce the Multipartite Thermal Pure Quantum (MTPQ) state, a generalization of the thermal pure quantum state to multipartite systems, and demonstrate that the entanglement structure in states of the multicopy SYK model exhibits finite-temperature $2$-uniform behavior.

This thesis investigates the interactions of partially massless (PM) fields in 4-dimensional (anti)de Sitter spaces, along with conformal higher spin fields and their coupling to matter in arbitrary dimensions. The first part of the thesis deals with PM fields and PM algebras. A reformulation of PM fields is proposed and studied using a novel chiral formulation, inspired by Penrose's twistor approach to massless fields in Minkowski space. This reformulation enables explicit construction of Yang-Mills-type interactions and current couplings. Next, an oscillator realisation for PM higher spin algebras is given in terms of bosonic and fermionic oscillators. The construction is based on the Weyl-Clifford algebra. The second part of the thesis derives the coupling between a massless scalar field and a background of higher spin fields within a manifestly covariant framework, employing Fedosov quantization techniques, called the "parent formulation". This formalism yields, in particular, an explicit covariant expression for the coupling between scalar fields and higher spin conformal gravity.

In quantum field theory, the algebraic existence of a field does not guarantee the existence of a corresponding localized asymptotic particle state. This distinction is well established in the presence of infrared effects, long-range correlations, and environmental interactions, and becomes particularly relevant in supersymmetric theories, where fermionic and bosonic degrees of freedom are constrained at the algebraic level but need not share identical asymptotic behavior. In this work we introduce a minimal and predynamical localization criterion that distinguishes algebraically allowed degrees of freedom from those capable of forming stable, phasecoherent asymptotic states. The criterion is formulated in terms of long-time stability under slow structural fluctuations of an effective background, without modifying the underlying field equations or introducing new physical interactions. We show that fermionic and scalar fields respond qualitatively differently to such structural effects. While fermionic modes may retain asymptotic stability, scalar modes generically exhibit decoherence and damping, preventing their interpretation as localized one-particle states. This provides a conservative and model-independent perspective on how supersymmetric algebraic structures may coexist with an asymmetric observable particle spectrum. The analysis is intentionally non-constructive and does not rely on specific supersymmetrybreaking mechanisms, cosmological assumptions, or new dynamical ingredients. Rather, it clarifies localization as an independent structural requirement for particle existence within standard quantum field theory.

We study the Coulomb branches of three-dimensional $\mathcal N=4$ quiver gauge theories of type $T_\rho(SU(N))$ associated with non-maximal nilpotent orbits of $SL(N)$. Using the Hall--Littlewood closed form for Coulomb-branch Hilbert series, together with independent checks from the monopole formula, we compute exact unrefined Hilbert series for all non-maximal partitions $\rho\vdash N$ with $N=4$, and extend the analysis to $N=5,6$. By analyzing the plethystic logarithms of the resulting Hilbert series, we find that in all cases examined the Coulomb branch is a complete intersection. The number of generators and relations follows a uniform pattern governed by the transpose partition $\rho^T$, with exactly $N-1$ relations appearing independently of $\rho$ in these examples. We summarize the results in explicit classification tables and formulate conjectures extending these patterns to arbitrary $N$. Our findings provide strong evidence for a remarkable uniformity in the algebraic structure of Coulomb branches within the $T_\rho(SU(N))$ family at low rank.

Motivated by bulk replica wormholes, we study the boundary effective theory that describes the near-horizon fluctuations of a near-extremal Reissner-Nordström black hole. This theory consists of a Schwarzian mode and a $U(1)$ phase mode. We compute the partition function of this boundary theory on replica geometries, from which the entropy is derived. Our analysis reveals a rich phase structure, in which the dominance of connected or disconnected replica configurations leads to a phase transition controlled by the temperature and the coupling constants $C$, $K$, and $\mathcal{E}$ of the 1d effective theory.

Topology plays a central role in classifying solitonic configurations in field theories, providing robustness and a nonperturbative label, the so-called topological charge $Q$. In soliton-fermion coupled systems, the relation between the topological charge and the number of zero modes is well established through the index theorem. However, the physical consequences of the sign of the topological charge have remained largely unexplored. In this work, we study fermions in $2+1$ dimensions coupled to Skyrmions with target space $\mathbb{C}\mathrm{P}^N$, particularly focusing on the backreactions of the fermions and on the sign of the topological charge. We obtain the solutions in a self-consistent manner, which exhibit an asymmetry with respect to the topological charge $\pm Q$ especially in the strong coupling regimes. This asymmetry is caused from the fermionic eigenvalue problem inherent in the self-consistent formulation. Although the Lagrangian is symmetric under $Q\to-Q$, the coupled equations for the Skyrmions and anti-Skyrmions become inequivalent once fermionic backreaction is taken into account. We demonstrate the mechanism in $\mathbb{C}\mathrm{P}^1$ and $\mathbb{C}\mathrm{P}^2$ Skyrmions, but the analysis is directly extendable for the general $\mathbb{C}\mathrm{P}^N$.

According to the island formula, information in the code subspace defined in the black hole interior is embedded in the Hawking radiation after the Page time. At first sight, this embedding suggests that operations acting on the Hawking radiation could modify the information in the code subspace, potentially leading to an apparent violation of causality. Indeed, in previous studies based on the PSSY model, which incorporates only the topological degrees of freedom of gravity, it was shown that when the error is sufficiently large, a violation of causality can arise, as indicated by a nonvanishing mutual information. In this paper, we investigate the situation in which dynamical gravity also acts on the Hawking radiation. In this case, operations on the Hawking radiation induce nontrivial backreaction on the bulk spacetime appearing in the gravitational path integral for the mutual information -- an effect that is absent when the Hawking radiation is non-gravitating. We find that this backreaction renders the relevant mutual information vanishing. This result implies that, in theories with dynamical gravity, the apparent violation of causality is resolved.

I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is reorganized by virtue of the linear terms that introduce the constraints via Lagrange multipliers, generalizing and giving results that cannot be obtained with the standard procedures which start at the quadratic terms. I apply the formalism to a theory of an $O(N)$-symmetric quantum field interacting with a ``classical" scalar field via cubic interactions in six spacetime dimensions. Using the renormalization group, I examine the effective potential, symmetry breaking with radiative corrections, the fixed points in $d=6-\epsilon$ dimensions, and compare with other works. Other possible generalizations and applications of the formalism are also discussed.

We review the structure of superconformal anomalies in 4d $\mathcal N$=4 conformal supergravity (CSG) coupled to a number N$_\rm v$ of $ \mathcal N$=4 vector multiplets and 6d (2,0) CSG coupled to N$_{_{\rm T}}$ of (2,0) tensor multiplets. Anomalies cancel if N$_\rm v$=4 and N$_{_{\rm T}}$=26 respectively. If the CSG part of the action is dropped and N$_{\rm v}$=6+ n$_{\rm v}$, the first theory is classically equivalent to the 4d $\mathcal N$=4 Poincaré supergravity (PSG) coupled to n$_{\rm v}$ vector multiplets, while the second one with N$_{_{\rm T}}$=5+ n$_{_{\rm T}}$ is classically equivalent to the 6d (2,0) PSG coupled to n$_{\rm T}$ tensor multiplets. We argue that these facts imply that divergences in the 4d PSG with n$_{\rm v}$ vectors should be proportional to n$_{\rm v}$+2 and similarly in the 6d PSG with n$_{_{\rm T}}$ tensors to n$_{_{\rm T}}$-21. These predictions appear to be consistent with known results of explicit scattering amplitude computations in these 4d and 6d PSG theories.

Polylogarithms on Riemann surfaces may be constructed efficiently in terms of flat connections that can enjoy various algebraic and analytic properties. In this paper, we present a single-valued and modular invariant connection ${\cal J}_\text{DHS}$ on the configuration space $\text{Cf}_n(\Sigma)$ of an arbitrary number $n$ of points on an arbitrary compact Riemann surface $\Sigma$ with or without punctures. The connection ${\cal J}_\text{DHS}$ generalizes an earlier construction for a single variable and is built out of the same integration kernels. We show that ${\cal J}_\text{DHS}$ is flat on $\text{Cf}_n(\Sigma)$. For the case without punctures, we relate it to the meromorphic multiple-valued Enriquez connection ${\cal K}_\text{E}$ in $n$ variables on the universal cover $\tilde \Sigma$ of $\Sigma$ by the composition of a gauge transformation and an automorphism of the Lie algebra in which ${\cal J}_\text{DHS}$ and ${\cal K}_\text{E}$ take values. In a companion paper, we shall establish the equivalence between the flatness of these connections and the corresponding interchange and Fay identities, for arbitrary compact Riemann surfaces.

Topological states of matter are characterized by nonlocal structures that are naturally encoded in the quantum entanglement of many-body wavefunctions. Topological semimetals are short-range entangled states at weak coupling and their entanglement structure at strong coupling remains largely unexplored. In this work, we investigate the multipartite entanglement structure of strongly coupled holographic nodal line semimetals. Building on previous studies of entanglement entropy and the holographic c-function, we focus on multipartite entanglement measures, including the conditional mutual information, multi-entropy, and the Markov gap which is based on the entanglement wedge cross section. Our results demonstrate that while these multipartite measures vanish in the long-distance limit $l \to \infty$, which confirms that the holographic nodal line semimetal remains a short-range entangled state, their large $l$ scaling behavior remains highly sensitive to the underlying topology. The large $l$ power-law decay and scaling exponents serve as robust, non-local order parameters that exhibit sharp changes at the quantum critical point. This work establishes multi-partite entanglement as a powerful probe of quantum topological phase transitions in strongly coupled topological systems.

We develop a general framework for constructing $2n$-site chiral integrable matrix product states in Aharony-Bergman-Jafferis-Maldacena spin chain, based on reflection equations and the fusion procedure. For four-site chiral integrable product states, we propose their exact overlap formulas with Bethe states. We also investigate the chiral integrable subspaces numerically.

The Cho-Maison monopole provides a monopole solution of the electroweak field equations, but possesses an infinite classical energy due to the Maxwell form of the hypercharge sector. Motivated by string-inspired effective field theories, we study the perturbative stability of the Cho-Maison monopole when the hypercharge kinetic term is regularised by a Born-Infeld extension, which renders the monopole energy finite. Focusing on the bosonic electroweak theory with an unmodified $SU(2)_L$ sector and a Born-Infeld U(1)_Y sector, we analyze linear fluctuations about the regularised monopole background. Using a complex tetrad and a spin-weighted harmonic decomposition, we reduce the fluctuation equations to coupled radial Schroedinger-type eigenvalue problems and examine the spectrum of the resulting operators. We extend the separation-of-variables framework developed by Gervalle and Volkov to this non-linear gauge-field setting. We show that, after appropriate gauge fixing and constraint elimination, the Born-Infeld deformation preserves the angular channel structure of the Maxwell theory and leads to a self-adjoint Sturm-Liouville type problem for the stability of the radial modes, with modified radial coefficients determined by the background Born-Infeld profile. The resulting operator represents a smooth deformation of the Maxwell case and retains positive kinetic weight. Our results provide plausible evidence for the stability of the Born-Infeld deformed monopole and, most importantly, a systematic framework for future numerical or variational studies aimed at a definitive spectral analysis.

We study shear fluctuations in non-relativistic holographic systems coupled to torsional Newton-Cartan geometry, using asymptotically Lifshitz spacetimes in Einstein-Maxwell-dilaton gravity. We identify a universal subdiffusive shear mode characterized by the quartic dispersion relation $\omega=-iD_4 k^4$, in sharp contrast to the conventional hydrodynamic diffusion. We derive this result analytically through a systematic higher-order matched asymptotic expansion connecting near-horizon and far-region solutions, and we verify it with direct numerical quasinormal mode calculations. Our numerics demonstrate that the first non-hydrodynamic mode is purely imaginary and gapped, following the dispersion relation $\omega=-i\omega_0-i D k^2$, and that both the hydrodynamic and the first non-hydrodynamic modes pass through pole-skipping points. These results highlight Lifshitz holography as an efficient framework for anomalous transport in strongly coupled non-relativistic quantum matter.

We study the behaviour of the conformal block expansions of scalar fivepoint Lorentzian conformal correlators in the limit where multiple cross ratios approach zero. Since this limit is controlled by intermediate operators with large spin, we use it to study the large spin expansion of the OPE coefficients involving these operators. By imposing bootstrap assumptions such as analyticity of the correlators, we derive an infinite set of new constraints on the large spin behaviour of OPE coefficients involving multiple spinning operators. We also show that for the case of $l=0$, these constraints can be trivialised to all orders in $1/J$ by identifying a pattern in the coefficients.

In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection matrix can shed some light on the nature of the canonical basis of a Feynman integral family, a concept still not fully understood in the general case. In particular we will show how the intersection matrix can detect hidden linear dependencies of the iterated integrals resulting from an $\eps$-factorized differential equation, which are difficult to find otherwise. Furthermore, we will explain how the intersection matrix can help in deriving (polynomial) relations between the transcendental functions occurring in the rotation to the canonical basis. This allows us to simplify the rotation, and furthermore leads to simplifications in the final result. The discussion we be kept as light as possible, focusing on a simple running example and deferring the technical details to the original publications.

We establish a relationship between the Davey--Stewartson II (DS II) integrable system in $(2{+}1)$ dimensions and quasi-exactly solvable planar interacting Dirac Hamiltonians that exhibit the super-Klein tunneling (SKT) effect. The Dirac interactions are constructed from the real and imaginary parts of breather solutions of the DS II system. In this framework, the SKT effect arises when the energy is tuned to match the constant background of the soliton, while the resulting Dirac Hamiltonians simultaneously support bound states embedded in the continuum. By imposing the SKT boundary conditions, we employ Darboux transformations to construct a general three-parameter family of DS II breather solutions that can be mapped to Dirac Hamiltonians. At the initial soliton time, the corresponding Dirac systems form a massless two-parameter family of Hermitian models with nontrivial electrostatic potentials. As the soliton time evolves, the systems become $\mathcal{PT}$-symmetric and develop a nontrivial imaginary mass term. Finally, when the soliton time is taken to be imaginary, the construction yields Hermitian Dirac systems that lack time-reversal symmetry. In all cases, we identify the emergence of quasi-symmetry transformations that preserve the SKT subspace of states while not commuting with the full Hamiltonian.

We study gauge theory based on the intermediate Lie algebra $E_{7+1/2}$, interpolating between $E_7$ and $E_8$. We propose a concrete UV completion via a 6d SCFT whose tensor branch description contains a pure $E_{7+1/2}$ gauge sector. The proposal is tested by 6d anomaly cancellation and by the 5d $\mathcal N=1$ Coulomb branch prepotential from the associated M-theory geometry. As a nonperturbative check, we determine the elliptic genus of the single-string worldsheet CFT using modular bootstrap. The result matches the vacuum character of the corresponding VOA for $E_{7+1/2}$, completing the elliptic genus/VOA correspondence along the Deligne-Cvitanović series.

We present the quantization of the electromagnetic field near the event horizon of a Schwarzschild black hole using Euclidean path integrals. Our result for the vacuum energy describes a black hole surrounded by a finite volume of photons at $T_{H} = \frac{1}{8\pi G M}$, the black hole quantum atmosphere. The total entropy includes contributions from this atmosphere, and the Bekenstein entropy, which arises from the Gibbons--Hawking--York boundary term, which encodes topological information. We show that the contribution of the quantum atmosphere to the black hole specific heat is positive, indicating that the system may become thermodynamically stable. By analyzing homology groups, we show that the black hole evaporation is a tunneling between topologically distinct spacetimes: Schwarzschild ($\chi = 2)$ transitions to the flat spacetime ($\chi = 1$) via Hawking radiation, where $\chi$ is the Euler characteristic, a topological invariant. This process resembles instanton-driven tunneling in Yang-Mills theories, where topologically non-trivial solutions dominate the vacuum amplitude. In our case, the Gibbons--Hawking--York term dominates the transition amplitude, which induces the evaporation process. These results corroborate the Parikh-Wilczek picture of Hawking radiation and the interpretation of Euclidean black holes as gravitational instantons.

We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields the complex binomial theorem which coincides with the Fourier transformation of the complex analogue of the Euler beta integral. At the bottom we obtain a Fourier transformation formula for the complex gamma function. This is done with the help of a new type of the limit $\omega_1+\omega_2\to 0$ (or $b\to \textrm{i}$ in two-dimensional conformal field theory) applied to the hyperbolic hypergeometric integrals.

We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit $\omega_1+\omega_2\to 0$ (or $b\to \imath$ in $2d$ CFT) and investigate in detail the two-particle case. Corresponding wave functions are described by complex hypergeometric functions in the Mellin-Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter $Q$-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special $\omega_1-\omega_2\to 0$ (or $b\to 1$) limit. Additionally, two new degenerations to the complex Calogero-Sutherland type models are described.

We propose a generalization of quantum field theory within Schrödinger's functional representation, inspired by Nambu's proper-time formulation of quantum mechanics. The key motivation for this generalization is to incorporate a fundamental, Lorentz-invariant minimum scale, which in this formulation is played by a minimal proper time $\tau_{\min}$. The introduction of $\tau_{\min}$ leads to several significant effects at very high energies: it modifies the Heisenberg uncertainty principle, induces a controlled violation of unitarity, and suppresses high-energy modes. This minimal scale renders the theory asymptotically safe through a mechanism akin to dimensional reduction, while reproducing all the standard results at low energies, where quantum field theory emerges. Remarkably, the same framework can accommodate a deterministic regime at energies approaching the Planck scale. These features suggest that a minimal proper-time formulation renders quantum field theory an effective but finite theory, superseded at trans-Planckian energies.

We study tight-binding models in the crossover from hyperbolic to Euclidean lattices, realized through the successive insertion of Euclidean defects into hyperbolic lattices. We analyze how the holographic two-point boundary correlation function and bulk density of states evolve as defects are gradually introduced. We find that bulk properties are strongly affected by the presence of Euclidean defects, whereas boundary observables remain remarkably robust even at high defect fractions. This robustness indicates that essential features of boundary physics on hyperbolic lattices, which capture aspects of AdS/CFT-like dualities in discrete systems, can be reproduced both experimentally and numerically without requiring perfectly hyperbolic lattices, thereby reducing the system size needed for implementation.

We study Weyl-invariant purely gravitational theories formulated within the Einstein-Cartan framework. In the Einstein-frame description, these models are dynamically equivalent to standard general relativity coupled to an axion-like pseudoscalar degree of freedom, which naturally drives a period of cosmic inflation. Without committing to a specific microscopic mechanism for reheating, we demonstrate that the post-inflationary reheating dynamics play a crucial role in shaping the inflationary predictions. In particular, we show that assumptions about the reheating temperature and the equation-of-state parameter can significantly affect the predicted values of inflationary observables, highlighting the necessity of consistently incorporating reheating effects in the phenomenological analysis of inflationary models.

This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the star-exponential with the quantum propagator for bosonic systems, this work develops the analogous extension for the fermionic case. A rigorous method, based on Grassmann variables and coherent states, is constructed to obtain a closed-form expression for the fermionic star-exponential from its associated propagator. As a primary application, a fermionic version of the Feynman-Kac formula is derived within this formalism, allowing for the calculation of the ground state energy directly in phase space. Finally, the method is validated by successfully applying it to the simple and driven harmonic oscillators, where it is demonstrated that a simplified ("naive") approach (with an ad-hoc "remediation") is a valid weak-coupling limit of the rigorous ("meticulous") formalism, thereby providing a new and powerful computational tool for the study of fermionic systems.

Although heavy-quark symmetry predicts a $B_1\bar{B}$ molecular partner of the $D_1\bar{D}$ molecule, no such state has been observed. We propose that the experimentally observed $\Upsilon(11020)$ may be a candidate for such a state, possibly containing a $B_1\bar{B}^{*}$ component. To test this, we interpret $\Upsilon(11020)$ as an $S$-wave $B_1\bar{B}$--$B_1\bar{B}^{*}$ molecule and compute its strong decay widths using the compositeness condition and effective Lagrangians. The couplings to $B_1$ and $\bar{B}^{(*)}$ are extracted by fitting $\Upsilon(11020)\to e^+ e^-$ and $\Upsilon(11020)\to \chi_{bJ} \pi\pi\pi$ data. Using these couplings, we evaluate partial widths into $B^{(*)}_{(s)}\bar{B}^{(*)}_{(s)}$, $\pi\pi \Upsilon(nS)$, $\pi\pi h_b(nP)$, and $\pi\pi\pi \chi_{b1}$ via hadronic loops, as well as three-body $B^{*}\pi \bar{B}^{(*)}$ decays via tree diagrams. The results indicate that $\Upsilon(11020)$ is predominantly a $B_1\bar{B}$ molecule, with its main decay channel being $B_s^{*}\bar{B}^{*}$. The $\pi\pi \Upsilon(nS)$ and $\pi\pi h_b(nP)$ widths are only a few eV, whereas $\pi\pi\pi \chi_{b1}$ reaches 0.167~MeV and the unobserved $\pi\pi\pi \chi_{b0}$ could be 0.754~keV. These distinctive decay patterns provide clear experimental signatures of the molecular nature of $\Upsilon(11020)$ and offer a test of heavy-quark symmetry.

Recent observations from the DESI Collaboration indicate a preference for quintom dark energy, i.e., its equation of state evolves across the cosmological constant boundary $w=-1$. It is well known that models with single perfect fluid or single scalar field minimally coupled to Einstein gravity develop perturbative instabilities around the crossing, thereby cannot realize the quintom scenario. In this paper, we provide a method to circumvent the instability problem of these models by introducing the coupling of dark energy to the Nieh-Yan density in teleparallel gravity. We show that with this coupling the background evolution is not affected, but the dark energy perturbation is removed from the menu of dynamical degrees of freedom, thus avoiding the intrinsic difficulties in the old models.

These are lecture notes for an introductory course on Nichols algebras. As a main reference, I work with the book by Heckenberger and Schneider, but I want to take a distinct categorical perspective and try to develop the topic for an audience without a background in Hopf algebras. On the other hand I put some emphasis on hands-on examples. My first goal is to explain the definitions and the striking properties of Nichols algebras, foremost the odd reflection theory that is already present in Lie superalgebras. My second goal is to explain how the category of representations of a quantum group can be constructed, using categorical tools, from the Nichols algebra as its centerpiece. This makes the zoo of different existing versions of quantum groups more transparent and allows the construction of many more non-semisimple modular tensor categories. Other topics include different types of examples beyond the diagonal case, categorical versions of some Hopf algebra constructions, and an outlook section on the appearance of Nichols algebras in conformal field theory.

In this paper, the quantum corrections to the kinematics of geometry, specifically geodesics, are presented. This is done by employing the path integral over the geodesics. Interestingly, the geodesics do not see any modifications in this framework. However for the distances, it is demonstrated that these quantum corrections exhibit distinct behaviors for time-like, light-like, and space-like geodesics. For time-like geodesics, the maximum correction is the Planck length, which disappears when the classical separation vanishes. The light-like geodesics do not exhibit quantum corrections, meaning that the causal light cone remains the same in both classical and quantum frameworks under certain conditions. The quantum corrections for space-like geodesics impose a minimum on space-like separation, potentially playing a role in removing singularities by preventing null congruences from being closer than the Planck length. This framework also explores the correspondence between space-like/time-like geodesics and quantum/statistical physics.

The standard $\delta N$ formalism, a cornerstone for calculating nonlinear curvature perturbations on super-Hubble scales, relies on the separate universe assumption, in which spatial gradients are neglected. However, this approximation breaks down in scenarios critical for primordial black hole formation, such as transitions to an ultra-slow-roll phase, where gradient interactions induce significant non-conservation of the comoving curvature perturbation. In this Letter, we introduce a framework that incorporates gradient corrections into the $\delta N$ formalism at a desired order by adding an effective source term to the background Klein--Gordon equation. This approach allows for a nonlinear treatment of curvature perturbations at the end of inflation considering initial conditions at the time of horizon exit. By computing the equilateral non-Gaussianity parameter $f_{\mathrm{NL}}^{\mathrm{eq}}$, we demonstrate that our method captures essential features missed by the standard $\delta N$, offering a simple yet rigorous pathway to determine nonlinear evolution expected from cosmological perturbation theory.

Nekrasov's gauge origami theory provides a (complex) 4-dimensional generalization of the ADHM quiver and its moduli spaces of representations. We describe the origami moduli space as the zero locus of an isotropic section of a quadratic vector bundle on a smooth space. This allows us to give an algebro-geometric definition of the origami partition function in terms of Oh--Thomas virtual cycles. The key input is the computation of a sign associated to each torus fixed point of the moduli space. Furthermore, we establish an integrality result and dimensional reduction formulae, and discuss an application to non-perturbative Dyson--Schwinger equations following Nekrasov's work. Finally, we conjecture a description of the origami moduli space in terms of certain 2-dimensional framed sheaves on $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, which we verify at the level of torus fixed points.

We construct higher-dimensional traversable wormholes in quasi-topological gravity (QTG) supported by a phantom scalar field. Using a static, spherically symmetric ansatz, we numerically analyze how quasi-topological gravity corrections affect the geometry and physical properties of the wormhole solutions. The resulting wormhole solutions are symmetric about the throat. Negative mass can arise for certain choices of parameters. For certain parameter ranges, the scalar charge $\mathcal{D}$ of the phantom field rapidly decreases with increasing the higher-curvature coupling parameter $\alpha$ and approaches zero. Moreover, by changing $\alpha$, the overall level of the Kretschmann scalar is also lowered. Finally, for sufficiently large $\alpha$, $-g_{tt}$ becomes close to zero near the throat, exhibiting a ``horizon''-like structure.

We uncover the physical nature of the electric and magnetic monopoles discovered by McGuire and Ruffini on Misner strings accompanying charged nutty black holes, showing that these strings carry singular, nonuniform flows of electric and magnetic fields. These fields inevitably have nonzero divergence, thereby simulating the effective electric and magnetic charge densities along the strings. The latter create a complex short-range electromagnetic hair zone around the horizon, making the combined Misner-Dirac strings classically observable. Typical features of this new type of hair are presented. We also note that rotation can act as a hair generator even in the absence of NUT.

Current observations indicate that an inverse exponential form of the inflaton potential provides an excellent description of single-field inflation. This potential fits the SPA$+$BK$+$DESI data sets well with in the $1\sigma$ bound in the $n_{\rm s}$-$r$ plane, thereby offering a simple and observationally viable single field inflationary scenario. To describe post-inflationary evolution and reheating, we extend the inverse exponential potential by adding a steep exponential term that remains negligible during inflation but becomes important afterwards. The resulting full potential develops a minimum after the end of inflation, leading to oscillations of the scalar field and consequently reheating of the Universe. We find that the maximum reheating temperature attainable in this scenario is of order $10^{13}\,\mathrm{GeV}$. The inverse exponential potential therefore emerges as a compelling candidate for early-Universe inflation, combining theoretical simplicity with robust observational viability.

The values of the Hubble constant ($\rm{H_0}$) inferred from the cosmic microwave background (CMB) and local measurements via the distance ladder exhibit a $\sim5\sigma$ tension. In this work we propose that the tension might be partially alleviated if a subcomponent of the dark matter undergoes decays triggered by spontaneous symmetry breaking in the dark sector, so that the equation of state parameter of the subcomponent shifts from $w \approx 0$ at early times to $w \approx -1/3$ at late times. We provide an effective field theory whose structure is partially motivated by the desire for a plausible UV completion. We find that such a construction naturally produces a possible self-interacting dark matter candidate with a velocity-dependent scattering cross section as a by-product of gauge invariance. This is relevant for addressing tensions between the predictions of $\Lambda$CDM and observations of small-scale structure, such as the core-cusp problem.

The short-duration gravitational-wave (GW) event GW231123 has inferred component masses in the pair-instability mass gap and exhibits a burst-like morphology with no clearly inspiral, making it an interesting target for tests beyond the standard binary black hole (BBH) interpretation. In this work, motivated by its phenomenological similarity to GW190521, we test whether GW231123 is compatible with a wormhole-echo scenario by modeling a leading echo pulse with a well-motivated phenomenological sine-Gaussian wavepacket. We perform Bayesian model comparison against a BBH baseline described by the IMRPhenomXPHM-SpinTaylor waveform, and obtain the Bayes factor ratio $\ln B^{\rm Echo}_{\rm BBH} = 1.87$, corresponding to weak-to-moderate support for the echo hypothesis. In our previous analysis for GW190521 within the same overall framework, we found $\ln B^{\rm Echo}_{\rm BBH} \approx -2.9$, implying a shift of $\Delta \ln B \approx 4.8$ between the two events. This sign change indicates that GW231123 is more compatible with a single-pulse echo description than GW190521.

In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an emergent phase-space description in which the Lanczos coefficients define an effective Hamiltonian governing operator motion along the Krylov chain. In the semiclassical limit, exponential complexity growth arises from hyperbolic trajectories, and asymptotically linear Lanczos growth appears as a universal chaotic fixed point, with sub-leading deformations classified as irrelevant, marginal or relevant. Going beyond the saddle, the Schwinger-Keldysh framework provides controlled access to fluctuations and large deviations of Krylov complexity, revealing sharp signatures of integrability-chaos crossovers that are invisible at the level of the mean. This formulation reorganises Krylov complexity into a dynamical field-theoretic framework and identifies new fluctuation diagnostics of operator growth in closed quantum systems.

In this work, we investigate the observable optical signatures of the Mod(A)Max black hole spacetime. We analyze key optical features, including the photon sphere, black hole shadow, and photon trajectories, and examine how these observables depend on the underlying geometric parameters, such as the electric charge and the Mod(A)Max coupling parameter. We further study the dynamics of neutral test particles in the vicinity of the black hole by deriving the effective potential within the Hamiltonian formalism. Using this potential, we obtain the specific energy and specific angular momentum for test particles on circular orbits of fixed radius, as well as the innermost stable circular orbit (ISCO), and explore how the geometric parameters influence these quantities and the ISCO radius. Finally, we derive the epicyclic (azimuthal, radial, and vertical) frequencies to analyze quasi-periodic oscillations (QPOs) exploring how the geometric parameters influences these and discuss their physical implications.

We present an effective field theory (EFT) framework for coupled-channel $B^{(*)}\bar D^{(*)}$ scattering, applying it to recent lattice QCD results by Alexandrou et al. [Phys. Rev. Lett. 132, 151902 (2024)]. Two complementary EFT approaches are developed: (1) A low-energy theory near the $B \bar D$ ($J=0$) and $B^* \bar D$ ($J=1$) thresholds, where coupled-channel effects are integrated out; (2) A coupled-channel formulation, where all relevant momentum scales are treated as soft, incorporating contact interactions and one-pion exchange (OPE). Importantly, OPE contributes to the lowest channels only through off-diagonal transitions, thus resulting in the appearance of the left-hand cut from two-pion exchange. The two approaches yield mutually consistent results, supporting the existence of shallow bound states in both channels, in agreement with the lattice findings. The finite-volume spectra and extracted pole positions show a near-degeneracy in $J=0$ and $J=1$ channels, consistent with heavy-quark spin symmetry (HQSS). Using HQSS, we predict additional shallow bound states near the $B \bar{D}^*$ and $B^* \bar{D}^*$ thresholds, which are accessible to future lattice simulations. The effect of OPE on the finite volume spectra is found to be small, with only moderate impact on HQSS partners.

This report is divided into three main parts: 1. The first two chapters discuss the emission of Short GRB (SGRB) from binary mergers surrounded by a strong magnetic field. By introducing our model, we investigated the physics of the emission of SGRBs from rotating and charged rotating BHs. A rapidly spinning, strongly magnetized neutron star (millisecond magnetar) is the primary source of strong magnetic fields ranging from $10^{13}~\rm to ~ 10^{16} G$. The decay of the magnetic field could power electromagnetic radiation, especially X-rays and gamma rays from NSs or NS-BH mergers as their primary sources. Considering the merger of compact bodies (NS-NS or NS-BH or BH-BH), we can obtain interesting results. 2. In the next two chapters, we reviewed the BH interiors to understand the nature of black hole interior information and evaporation from its initial to final phases via entropy variation. The evolution relation obtained from two types of entropy gives diverse understandings of the evaporation of BHs under Hawking radiation. 3. The fifth Chapter is related to BH configuration (information) entropy and the thermodynamic phase transition of $f(R)$ BH. Here, we consider a d$-$dimensional black hole (BH) in $f(R)$ gravity and analyze the effect of modified gravity on critical point parameters, the difference in number densities, and configuration entropy during the BH phase transition phenomenon. These results were also compared with charged AdS BH, the holographic dual of van der Waal's fluid, and hence the BH in modified gravity.

We generalize the spectral-function formalism to describe two-nucleon knockout processes in exclusive kinematics. Significant improvements are introduced both in the treatment of the current operators entering the $\Delta$-current contribution and in the modeling of correlations between the two struck nucleons, including a consistent treatment of isospin dependence and the explicit incorporation of angular correlations. The framework is validated through comparisons with relativistic Fermi-gas calculations and with semi-exclusive electron-nucleus scattering data. Our results demonstrate that an accurate description of nuclear dynamics plays a crucial role in modeling this reaction mechanism. We further present a study of selected electroweak observables relevant to neutrino-scattering experiments.

Collective excitations of Fractional Quantum Hall (FQH) liquids at long wavelengths are thought to be of a generally covariant geometric nature, governed by area-preserving diffeomorphisms ($\mathrm{SDiff}$). But current analyses rely solely on the corresponding perturbative $w_\infty$ Lie algebra. We argue this is insufficient: We identify a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory which carries unitary $\mathrm{SDiff}$ equivariance. But this turns out to be non-differentiable, suggesting FQH excitation phenomenology beyond the $w_\infty$ algebra.

We continue studying of global conformal blocks on the torus in a special (necklace) channel. Functions of such multi-point blocks are explicitly found under special conditions on the blocks' conformal dimensions. We have verified that these blocks satisfy the Casimir equations, which were derived in previous studies.

Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS particles'', exemplified by certain Cohomological Hall Algebras. We conjecture the existence of a monoidal functor from the category of line defects to a certain category of bimodules for the BPS Algebra in any Coulomb vacuum. We describe images of simple objects under the conjectural functor and study their monoidal structure in examples. We conjecture that the functor may be an equivalence of dg-categories and test the conjecture at the level of the equivariant Witten indices of the spaces of morphisms.

It is widely believed, and axiomatically postulated in mathematical quantum field theory, that the vacuum is a unique vector state. The recent solution of the quantum Yang-Mills theory of the strong interaction revealed the presence of two vacua and a mixed quantum state. The second, confining vacuum, is an eigenstate of an auxiliary field, with a non-zero eigenvalue, as opposed to the zero eigenstate of the perturbative vacuum, and provides a new mechanism of scale generation. I show that this non-trivial vacuum structure implies confinement, in the sense that vacuum expectation values between states separated at large, space-like distances, tend to zero, whereas in ordinary quantum theories with a unique vacuum, they are known to satisfy the cluster decomposition principle, and tend to free, asymptotic states, at large separations. In a confined state, the correlation functions are zero at spacelike distances larger than the scale of the theory. Accordingly, they can be non-zero only along a timelike worldline (with an associated spacelike width). The theory is by construction unitary and Lorentz invariant, but the different vacua give a direct sum decomposition. Implications on determinism and causality, and generalizations of the confinement mechanism for theories with other symmetries and interactions are discussed. I argue that confinement, in the generalized sense, is a necessary (certainly not sufficient) condition for proposed theories of a conscious state. Also, I discuss the relation with the measurement postulate of quantum mechanics (when the ``observer" is merely a detector). I argue that confinement, in the strong interaction, is an important mechanism, similar to and possibly along with decoherence, for the measurement process.

The Lanczos algorithm offers a framework for constructing wave functions in closed and open quantum systems from their Hamiltonians. Since the early universe is inherently an open system, we employ this algorithm to investigate Krylov complexity across various cosmological phases: inflation, radiation domination (RD), and matter domination (MD). Our results highlight a clear distinction in Krylov complexity between the closed- and open-system methodologies. To accurately capture the influence of potentials during RD and MD, we examine a set of inflationary potentials, including the Higgs potential, $R^2$ inflation, and chaotic inflation, while incorporating violations of slow-roll conditions. This study is conducted in conformal time through the preheating stage. Numerically, we find that the evolution of Krylov complexity and Krylov entropy shows remarkable similarity across different potentials during RD and MD. Furthermore, we rigorously construct an open two-mode squeezed state using the second kind of Meixner polynomial. Based on this construction, we derive for the first time the evolution equations for the squeezing parameter $r_k$ and phase $\phi_k$ in terms of the scale factor. Our analysis indicates that dissipative effects lead to rapid decoherence-like behavior. In addition, we observe that the inflationary universe behaves as a strongly dissipative system, whereas during the RD and MD epochs the universe exhibits weak dissipative characteristics. This work opens new perspectives for studying the universe from a quantum-informational viewpoint.

In this work, we relate two recent constructions that generalize classical (genus-zero) polylogarithms to higher-genus Riemann surfaces. A flat connection valued in a freely generated Lie algebra on a punctured Riemann surface of arbitrary genus produces an infinite family of homotopy-invariant iterated integrals associated to all possible words in the alphabet of the Lie algebra generators. Each iterated integral associated to a word is a higher-genus polylogarithm. Different flat connections taking values in the same Lie algebra on a given Riemann surface may be related to one another by the composition of a gauge transformation and an automorphism of the Lie algebra, thus producing closely related families of polylogarithms. In this paper we provide two methods to explicitly construct this correspondence between the meromorphic multiple-valued connection introduced by Enriquez in e-Print 1112.0864 and the non-meromorphic single-valued and modular-invariant connection introduced by D'Hoker, Hidding and Schlotterer, in e-Print 2306.08644.

We compute correlation functions of the primordial density perturbations when they couple to a gapless, strongly coupled sector of spectator fields -- ``unparticles" -- during inflation. We first derive a four-point function of conformally coupled scalars for all kinematic configurations in de Sitter, which exchanges an unparticle at tree-level, by performing direct integration using the Mellin-Barnes method. To obtain inflationary bispectra and trispectra, we apply weight-shifting operators to the conformally coupled scalar correlator. We show that the correlators solve differential equations determined by the additional symmetries enjoyed by the unparticle propagator. Based on these differential equations, we are able to discuss the spinning-unparticle exchanges, focusing on two possible cases where the currents or the stress tensor of unparticles are coupled to inflatons, with the help of spin-raising operators. Finally, we study the phenomenology of the resulting shape functions. Depending on the value of the unparticle scaling dimension, we classify three characteristic shapes for the inflationary bispectra, including near-equilateral, near-orthogonal, and a novel shape which appears when the scaling dimensions are close to half-integers. More generally, we find that the leading order squeezed limits are insufficient to conclusively determine the detection of a light particle or unparticle. Only the full shapes of bispectra and trispectra can break this degeneracy.

The moduli space of self-dual $SU(N)$ Yang-Mills instantons on $\mathbb T^4$ of topological charge $Q = r/N$, $1 \leq r \leq N-1$, is of current interest, yet is not fully understood. In this paper, starting from 't Hooft's constant field strength ($F$) instantons, the only known exact solutions on $\mathbb T^4$, we explore the moduli space via analytical and lattice tools. These solutions are characterized by two positive integers $k, \ell$, $k+\ell=N$, and are self-dual for $\mathbb T^4$ sides $L_\mu$ tuned to $k L_1 L_2 = r \ell L_3 L_4$. For gcd$(k,r) = r$, we show, analytically and numerically (for $N = 3$) that the constant-$F$ solutions are the only self-dual solutions on the tuned $\mathbb T^4$, with $4r$ holonomy moduli. In contrast, when gcd$(k,r) \ne r$, we argue that the self-dual constant-$F$ solutions acquire, in addition to the $4\text{gcd}(k,r)$ holonomies, $4r - 4\text{gcd}(k,r)$ extra moduli, whose turning on makes the field strength nonabelian and non-constant. Thus, for gcd($k,r) \ne r$, 't Hooft's constant-$F$ solutions are a measure-zero subset of the moduli space on the tuned $\mathbb T^4$, a fact explaining a puzzle encountered in arXiv:2307.04795. We also show that, for $r = k = 2$, $N = 3$, the agreement between the approximate analytic solutions on the slightly detuned $\mathbb T^4$ and the $Q=2/3$ self-dual configurations obtained by minimizing the lattice action is remarkable.

Recent work has demonstrated that Euclidean Giddings-Strominger axion wormholes are stable in asymptotically flat 4D Minkowski spacetime, suggesting that they should, at least naively, be included as contributions in the quantum gravitational path integral. Such inclusion appears to lead to known wormhole paradoxes, such as the factorization problem. In this paper, we generalize these results to AdS3 spacetime, where the axion is equivalent to a U(1) gauge field. We explicitly construct the classical wormhole solutions, show their regularity and stability, and compute their actions for arbitrary ratios of the wormhole mouth radius to the AdS radius and across various topologies. Finally, We discuss potential implications of these findings for the 3D gravitational path integral.

One approach to analyzing entanglement in a gauge theory is embedding it into a factorized theory with edge modes on the entangling boundary. For topological quantum field theories (TQFT), this naturally leads to factorizing a TQFT by adding local edge modes associated with the corresponding CFT. In this work, we instead construct a minimal set of edge modes compatible with the topological invariance of Chern-Simons theory. This leads us to propose a minimal factorization map. These minimal edge modes can be interpreted as the degrees of freedom of a particle on a quantum group. Of particular interest is three-dimensional gravity as a Chern-Simons theory with gauge group SL$(2,\mathbb{R}) \times$ SL$(2,\mathbb{R})$. Our minimal factorization proposal uniquely gives rise to quantum group edge modes factorizing the bulk state space of 3d gravity. This agrees with earlier proposals that relate the Bekenstein-Hawking entropy in 3d gravity to topological entanglement entropy.

In this paper, we study complex-valued neural network (CVNNs) with tensor-valued hidden-to-output weights within the framework of neural-network quantum field theory (NN-QFT). For standard CVNNs with scalar weights, we derive the generating functional and identify the exact Gaussian process that arises in the infinite-width limit, together with its associated effective quantum state. When the last-layer weights are promoted to Clifford-algebra-valued tensors, the network output becomes complex matrix-valued, and a fermion-like sign structure in the large-width correlation functions of the network output is induced. We show that, in the infinite-width limit, correlators with equal numbers of $f^†$ and $f$ obey fermionic Wick rules and can be written as determinants built from a scalar Euclidean kernel $S(x,y)=\langle f^†(x)f(y)\rangle$. This provides a sign-structured extension of NN-QFT at the level of Euclidean correlators and Feynman rules, even though a microscopic Grassmann path integral representation for the network parameters has not yet been constructed. Our analysis thus pushes the NN-QFT correspondence beyond purely bosonic Gaussian fields and suggests a possible route to encoding fermion-like symmetries in neural architectures for QFT correspondence.

Recent studies have shown that a spatially random Yukawa-type interaction between a Fermi surface and critical bosons can produce linear-in-temperature resistivity, the defining signature of strange metals. In this article, we systematically classify all scalar couplings of the form $(\psi^{\dagger}\psi)^n\phi^m$ in arbitrary dimensions to identify possible candidates for strange-metal behaviour within this disordered framework. We find that only spatially random Yukawa-type interaction in $(2+1)$ dimensions can yield linear resistivity.

We discuss scalar field theories with potentials V({\phi})=\k{appa}({\phi}^2)^{\nu} for generic {\nu}. We conjecture that these models evade various no-go theorems for scalar fields in four spacetime dimensions.

We formulate interacting antisymmetric tensor gauge theory in a configuration space consisting of a pair of dual field strengths which has a natural symplectic structure. The field equations are formulated as the intersection of a pair of submanifolds of this infinite-dimensional symplectic configuration space, one of which is a Lagrangian submanifold while the other is either a coisotropic or Lagrangian submanifold, depending on the topology. Chern-Simons interactions give the configuration space an interesting global structure. We consider in detail the example of a six-dimensional theory of a 3-form field strength coupled to Yang-Mills theory via a Chern-Simons interaction. Our approach applies to a broad class of gauge systems.

We uncover a surprising universal soft behaviour (USB) of a de Sitter (dS) S-matrix for \textit{all} exceptional effective field theories (EFTs) in dS space, stemming from the recently proposed generalised energy conservation (GEC) condition. At leading order in the soft limit, the dS S-matrices for all exceptional EFTs in four spacetime dimensions exhibit no scaling with the soft momentum, i.e. $\lim_{k\rightarrow 0}\mathcal{A}(k)\sim\mathcal{O}(1)$, a feature we term USB. We specifically show that USB fixes the four-point amplitudes in Dirac-Born-Infeld (DBI) theory and Special Galileon, and six-point amplitude in $SU(N)$ Non-Linear Sigma Model (NLSM) given the minimal derivative count. We then conjecture USB fixes the interactions of all exceptional EFTs to all orders, thereby providing a unification criterion for them. Our result further underpins the idea that $\Delta\geq 4$ exceptional theories in dS are characterised by the spectrum and stability requirement alone, resonating with the low energy theory of gravity--General Relativity.

A finite formulation of quantum field theory based on a system of differential equations reminiscent of the Callan-Symanzik equations is discussed. This system of equations was previously formulated in the bare language. We rederive it in a fully renormalized language. For the latter, within a simple $\phi^4$ toy model, it is shown that with a specific choice of renormalization conditions - namely, the on-shell scheme for the renormalized mass - this class of finite renormalization prescriptions is equivalent to the standard renormalization-group equation written in the Callan-Symanzik-Ovsyannikov form.

We investigate tricritical phase transitions in a holographic model of topological superconductivity using Einstein-Maxwell gravity coupled with a charged scalar field in Anti-de Sitter spacetime. By incorporating both gravitational backreaction and quartic self-interaction $V(\phi) = \lambda \phi^4$, we demonstrate that the system exhibits both second-order and first-order phase transitions separated by a tricritical point at $(q_{\mathrm{tri}},T_{\mathrm{tri}})=(2.00\pm0.02,0.1521\pm0.0003)$ in the $(q,T)$ parameter space, where $q$ is the dimensionless charge parameter. The backreacted critical temperature shows enhancement by a factor of 1.22 compared to the probe limit, revealing the importance of strong coupling effects. Tricritical scaling analysis yields an exponent $\phi=0.40\pm0.03$, deviating significantly from mean-field predictions ($\phi=2/3$) due to finite-size effects and holographic geometric corrections. The order parameter critical exponent $\beta=0.50\pm0.02$ remains consistent with mean-field theory due to large-$N$ suppression of quantum fluctuations. The frequency-dependent conductivity exhibits a superconducting gap with energy ratio $\omega_{g}/T_{c}=3.18\pm0.05$, representing a $10\%$ deviation from BCS theory. Holographic entanglement entropy provides quantum information signatures that clearly distinguish transition types. Our results establish that gravitational backreaction, combined with scalar self-interaction, is essential for generating tricritical behavior in holographic superconductors.

In this paper, we investigate thermodynamical aspects of a novel static non-extremal black hole solution in the five-dimensional anti-de Sitter (AdS) space carrying four independent electric charge parameters and with a negative cosmological constant, within the framework of $D=5$, $\mathcal{N} = 2$ gauged supergravity coupled to three vector multiplets specified by the pre-potential $\mathcal{V} = STU -W^2U \equiv 1$. A central outcome of our work is the demonstration that the thermodynamics of this solution consistently satisfies both the differential and integral forms of the first law of black hole thermodynamics. When the fourth charge is set to zero, our configuration reduces to the known three-charge static non-extremal AdS$_5$ black hole within the gauged $STU$ model, and its thermodynamic behavior connects smoothly to that limit. Finally, we also provide a brief discussion about topological classifications of its thermodynamics.

Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation $J_W$, quantum discord $D_W$, and one-shot distillable entanglement $E_D$, defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts -- measurement-based correlations and one-shot distillable entanglement -- while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.

We develop a basis--covariant one--loop renormalization framework for two interacting real scalars in $D=4-\epsilon$ with the most general two--derivative Lorentz--violating quadratic form, allowing anisotropic spatial gradients and direction--dependent kinetic mixing, together with general cubic and quartic interactions forming RG complete set of operators at one-loop. In dimensional regularization with minimal subtraction we compute the full set of one--loop UV divergences and obtain closed beta functions for quartic and cubic couplings, masses. The pole coefficients admit a universal spectral representation as angular averages over the direction--dependent eigenvalues and projectors of the UV kinetic matrix; all anisotropy dependence enters through a single universal kernel admitting two--particle phase--space interpretation. We classify fixed points and fixed manifolds and show, in particular, that anisotropy restricts the existence of the coupled Wilson--Fisher--type fixed point. When the cross--gradients are turned on the coefficients in beta functions are governed by six phase--space weights admitting interpretation in terms of encoding ``populations'' and ``coherences'' of the UV normal modes.

We formulate matter-coupled scaling-Carroll gravity as a gauge theory and analyze its associated gravity multiplet. After fixing the scaling symmetry, the theory is governed by the trace of the extrinsic curvature, the Carroll boost symmetry, and a vector field descending from dilatation. We show that appropriate gauge choices and geometric constraints lead to distinct regimes, including dynamical Carroll gravity, Aristotelian gravity, and a fracton gauge theory coupled to Aristotelian geometry. In the fracton phase, the Carroll boost parameter plays the role of a vector-charge gauge symmetry.

We introduce generalisations of von Neumann entanglement entropy that are invariant with respect to certain scale transformations. These constructions are based on the Unit-Invariant Singular Value Decomposition (UISVD) in its left-, right-, and bi-invariant incarnations, which are variations of the standard Singular Value Decomposition (SVD) that remain invariant under the corresponding class of diagonal transformations. These measures are naturally defined for non-Hermitian or rectangular operators and remain useful when the input and output spaces possess different dimensions or metric weights. We apply the UISVD entropy and discuss its advantages in the physically interesting framework of Biorthogonal Quantum Mechanics, whose important aspect is indeed the behaviour under scale transformations. Further, we illustrate features of UISVD-based entropies in other well-known setups, from simple quantum mechanical bipartite states to random matrices relevant to quantum chaos and holography, and in the context of Chern-Simons theory. In all cases, the UISVD yields stable, physically meaningful entropic spectra that are invariant under rescalings and normalisations.

We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the $\phi^4$ theory near four dimensions and $\phi^6$ near three dimensions, semiclassically determining the full spectrum of neutral operators in the traceless symmetric Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.

We consider 4-point $W_3$ classical blocks focusing on the blocks level-1 and level-2 semi-degenerate operators. We derive BPZ-type equations for the auxiliary 5-point blocks with one additional fully degenerate operator. The monodromy properties of these equations are encoded by the accessory parameters, related to the 4-point $W_3$ classical blocks. We solve the BPZ-type equations via heavy-light perturbation theory and find the accessory parameters, which allows us to obtain the explicit expressions for the considered class of classical blocks.

Following the idea of Refs.[1,2], the double-copy-like decomposition of exchanged internal states in the world-line limit of one-loop string amplitudes is systematically formulated and generalized to both bosonic and heterotic string theories. As an application, the one-loop beta functions for the gauge and gravitational coupling constants are investigated by analyzing the low-energy field-theory limit of the corresponding three-point one-loop amplitudes in heterotic string theory under a naive $T^6$ compactification. Due to supersymmetry, these beta functions vanish trivially. However, by decomposing the scattering integrand according to the different internal loop-exchanged states, the most general model-independent results are obtained.

In this note, we explore computational algebraic geometry techniques to compute $14^{th}$ Helicity Trace Index of 4-charge, $\frac{1}{8}$-BPS, $\mathcal{N}=8$ pure D-brane configurations dual to D1-D5-P-KK monopole dyonic black holes. We extend the analysis of our previous work to higher values of charges and address subtleties involving compatible gauge choices for $(1,1,1,N)$ charge configurations. For explicit SUSY state counting, we use a parametric monodromy method for the 4-charge $(1,1,1,5)$ and $(1,1,1,6)$ configurations and find that the results match the U-dual picture. By a different choice of the R-symmetry representations, it is possible to explicitly break all supersymmetry and study related (non-)abelian versions as 4-charge non-BPS pure D-brane systems. Using analytical Gröbner bases, we show that the potential has no zero energy configuration. The higher end of the spectrum asymptotes towards the Coulomb branch local minima submanifold representing unbounded D-brane configurations, and the Mixed branch local minima represent bound states at parametrically lower values of the potential. In between, there are several marginally bound stabilizer submanifolds representing partially bounded D-brane configurations. We developed physics-inspired computational techniques to deform the potentials and lift flat directions, thereby cataloging the energy landscape and counting the low-energy stable states with degeneracy.

We show that the type-A conformal anomaly in $2n$ dimensions follows from standard Stora-Zumino descent, starting from the Euler invariant polynomial for the Euclidean conformal group $SO(2n+1,1)$ in $6d$, thereby placing type-A anomalies on the same footing as ordinary perturbative t Hooft anomalies. We discuss implications for anomaly inflow, and t Hooft anomaly matching for the full conformal group with a Wess-Zumino-Witten term. In 4d, this enables the construction of a dilaton effective action matching the full type-A $SO(5,1)$ conformal anomaly.

In this study, we examine the role of the repulsive Casimir force in counteracting the gravitational contraction of a thin spherically symmetric shell. Our main focus is to explore the possibility of achieving a stable balanced configuration within the theoretically reliable weak field limit. To this end, we consider different types of Casimir forces, including those generated by massless scalar fields, massive scalar fields, electromagnetic fields, and temperature-dependent fields.

This article delves into the observational signatures and theoretical underpinnings of rotating astrophysical objects, with a particular focus on superspinars -exotic objects characterized by the absence of event horizons due to their high angular momentum. While solutions within General Relativity (Kerr superspinars) predict such objects, their classical forms harbor naked singularities, violate causality, and exhibit problematic repulsive gravitational effects. These characteristics render classical superspinars theoretically objectionable, leading to the consideration of them as physically implausible. On the other hand, the incompatibility between General Relativity and Quantum Mechanics suggests the exploration of alternative models, particularly those in which Quantum Gravity dominates the core and prevents the formation of scalar curvature singularities. This work demonstrates that superspinars without scalar curvature singularities can avoid all the complications associated with Kerr superspinars. Moreover, from a phenomenological standpoint, it is shown that the silhouettes of these superspinars could be markedly distinct from those of black holes and classical Kerr superspinars. To substantiate these differences, we perform a comprehensive analysis of inner null geodesics and investigate the structure of the Planckian region within superspinars without scalar curvature singularities. Our study reveals that only these superspinars provide the potential for distant observers to directly observe the extremely high curvature regions within their interiors.

Under the existence of a massless spinor with respect to the total connection in a spacetime modeled as a Lorentzian manifold with internal boundaries, such as finite volume semi-classical Black Holes, we show that a topological mechanism naturally induces terms in the Einstein-Cartan gravitational action that can be interpreted as General Relativity with dark energy. This may alleviate the problems of dark energy. The topological information is carried by a harmonic 1-form associated to the first co-holomology group of the spacetime, which induces a spacetime contortion acting on the horizontal bundle.

We investigate (3+1)d topological orders in fermionic systems with an anomalous $\mathbb{Z}_{2N}^{\mathrm{F}}$ symmetry, where its $\mathbb{Z}_2^{\mathrm{F}}$ subgroup is the fermion parity. Such an anomalous symmetry arises as the discrete subgroup of the chiral U(1) symmetry of $\nu$ copies of Weyl fermions of the same chirality. Inspired by the crystalline correspondence principle, we deform the anomalous $\mathbb{Z}_{2N}^\mathrm{F}$ symmetry of (3+1)d Weyl fermion to the anomalous $C_N \times \mathbb{Z}_2^\mathrm{F}$ symmetry. Then we microscopically construct symmetry-preserving gapped boundary states of the closely-related (4+1)d $C_N\times \mathbb{Z}_2^{\mathrm{F}}$ symmetry-protected topological (SPT) state (with $C_N$ being the $N$-fold rotation), whenever it is possible. In particular, for $\nu=N$, we show that the (3+1)d symmetric gapped state admits a topological $\mathbb{Z}_4$ gauge theory description at low energy, and propose that a similar theory saturates the corresponding $\mathbb{Z}_{2N}^\mathrm{F}$ anomaly. For $N \nmid \nu$, our construction admits no topological quantum field theory (TQFT) symmetric gapped state; while for $\nu=N/2$, we find a non-TQFT symmetric gapped state via stacking lower-dimensional (2+1)d non-discrete-gauge-theory topological order inhomogeneously. For other values of $\nu$, no symmetric gapped state is possible within our construction, which is consistent with the no-go theorem by Cordova-Ohmori.

We discuss the emission of radiation from general sources in quantum scalar, electromagnetic and gravitational fields using the Rindler coordinate frame, which is suitable for a uniformly accelerated observer, in the Minkowski vacuum. In particular, we point out that, to recover the usual Larmor radiation in the interaction picture, it is necessary to incorporate the Unruh effect. Thus, the observation of classical Larmor radiation could be seen as vindicating the Unruh effect in the sense that it is not correctly reproduced in this context unless the Unruh effect is taken into account.

We present a new approach to the conservative dynamics of binary systems, within the effective one-body (EOB) framework, based on the use of a Lagrange multiplier to impose the mass-shell constraint. When applied to the post-Minkowskian (PM) description of the two-body problem in Einsteinian gravity, this Lagrange-EOB (LEOB) approach allows for a new formulation of the conservative dynamics that avoids the drawbacks of the recursive definition of EOB-PM Hamiltonians. Using state-of-the-art expressions of the resummed waveform and radiation reaction, we apply our new formalism to the construction of an aligned-spin, quasi-circular, inspiraling EOB waveform model, called {\tt LEOB-PM}, that incorporates analytical information up to the 4PM level, completed by 4PN contributions up to the sixth order in eccentricity, in the orbital sector, and by 4.5PN contributions, in the spin-orbit sector. In the nonspinning case, we find that an uncalibrated LEOB-PM model delivers maximum EOB/NR unfaithfulness ${\bar{F}}_{\rm EOBNR}$ (with the Advanced LIGO noise in the total mass range $10-200M_\odot$) varying between $0.2\%$ and $1\%$ over all the nonspinning dataset of the Simulating eXtreme Spacetime (SXS) Numerical Relativity (NR) catalog up to mass ratio $q=15$. It also delivers excellent phasing agreement with the $q=32$ configuration of the RIT catalog. We also found consistency between binding energies within a few percent at the NR merger location. Then, when NR-informing the dynamics of the model (both orbital and spinning sectors) by using 17 SXS dataset, we find that the EOB/NR unfaithfulness (compared to 530 spin-aligned SXS waveforms) has a median value of $5.39\times 10^{-4}$, or $6.13\times 10^{-4}$ (depending on the spin-spin interactions), reaching at most $\sim 1\%$ in some of the high-spin corners.

We study parity violation in the early universe by examining the four-point correlation function within the axion inflation model. Using an open quantum system formalism from our previous work, we calculate the influence functional to fourth order, from which we then derive the inflaton four-point correlation function. When we decompose this function using isotropic basis functions, the expansion coefficients $\zeta_{\ell',\ell'',\ell'''}$ naturally split into parity-even and parity-odd components. In the large $\xi$ approximation, which enhances the production of right-handed photons in the model, the derivation of these coefficients simplifies. We work out the lowest-order nonvanishing parity-odd $\zeta_{234}$ term which clearly indicates the presence of parity violation. Moreover, our derived values of the coefficients are consistent with recent observational data from galaxy surveys.

The (emergent) symmetry of a critical point is one of the most important information to identify the universality class and effective field theory, which is fundamental for various critical theories. However, the underlying symmetry so far can only be conjectured indirectly from the dimension of the order parameters in symmetry-breaking phases, and its correctness requires further verifications to avoid overlooking hidden order parameters, which by itself is also a difficult task. In this work, we propose an unbiased way to numerically identify the underlying (emergent) symmetry of a critical point in quantum many-body systems, without prior knowledge about its low-energy effective field theory. Through calculating the reduced density matrix in a very small subsystem of the total system numerically, the Anderson tower of states in the entanglement spectrum clearly reflects the underlying (emergent) symmetry of the criticality. It is attributed to the fact that the entanglement spectrum can observe the broken symmetry of the entanglement ground-state after cooling from the critical point along an extra temperature axis.

We present a physically motivated dark-energy (DE) model rooted in the topological structure of the Quantum ChromoDynamic (QCD) vacuum. In this framework, DE arises from the difference between the vacuum energy of an expanding FRW universe and Minkowski spacetime, induced by QCD topological sectors. The resulting DE term in the Friedmann equation scales with the Hubble rate, $\rho_{\rm DE}(t)\propto H(t)$, once DE dominates cosmic expansion, i.e. when the Universe is close to the de Sitter regime with $H\approx$ constant. The QCD scale, $\Lambda_{\rm QCD}\sim100~{\rm MeV}$, naturally fixes the DE density and explains why its influence becomes significant only recently. The construction relies solely on the Standard Model of particle physics, introducing no new fields or couplings. The most fundamental change is the possibility of modifying the evolution of the background cosmology in the Friedmann equation. Key predictions include: (a) A present-day equation of state parameter $w_{\rm DE,0}>-1$ that asymptotically approaches the de Sitter limit $w_{\rm DE}=-1$ in the future. (b) A present-day Hubble constant $H_0$ that asymptotically approaches a constant $\overline{H}$ set by $\Lambda_{\rm QCD}$. (b) For $z\ge 0$, $w_{\rm DE}(z)$ may lie above or below $-1$ and can cross this boundary multiple times at different $z$, behavior qualitatively consistent with the recent DESI findings. (c) In our framework, any deviation from $\Lambda$CDM leads to a corresponding deviation of $H(z)$, which can be tested with existing and future cosmological observations.

We show that two Yukawa-SYK models with a weak tunneling contact can have an exotic hybrid superconducting thermofield-double-like state that is holographically dual to a traversable wormhole connecting two black holes with charged scalar hair. The hybrid superconducting thermo-field-double/wormhole state is distinguishable by anomalous scaling of revival oscillations in the fermionic Green's function, but also in a unique Andreev-revival in the anomalous Green's function. The existence of this TFD/wormhole state surprisingly shows that the some quantum critical effects can survive the phase transition to superconductivity. This Andreev-revival is in principle an accessible signature of the transition to the TFD/wormhole phase detectable in the ac-Josephson current.

We define entropic marginally outer trapped surfaces (E-MOTSs) as a generalization of apparent horizons. We then show that, under first-order perturbations around a stationary black hole, the dynamical black hole entropy proposed by Hollands, Wald, and Zhang, defined on a background Killing horizon, can be expressed as the Wall entropy evaluated on an E-MOTS associated with it. Our result ensures that the Hollands-Wald-Zhang entropy reduces to the standard Wald entropy in each stationary regime of a dynamical black hole, thereby reinforcing the robustness of the dynamical entropy formulation.

The exponential-tail behaviours of the probability density function (PDF) of the primordial curvature perturbation are confirmed in the mild-waterfall variants of hybrid inflation with the use of the stochastic formalism of inflation. On top of these tails, effective upper bounds on the curvature perturbation are also observed, corresponding to the exact hilltop trajectory during the waterfall phase. We find that in the model where the leading and higher-order terms in the expansion of the inflaton potential around the critical point are fine-tuned to balance, this upper bound can be significantly reduced, even smaller than the primordial black hole (PBH) threshold, as a novel perturbation-reduction mechanism than the one proposed by Tada and Yamada. It makes PBH formation much difficult compared to the Gaussian or exponential-tail approximation. We also introduce Johnson's $S_U$-distribution as a useful fitting function for the PDF, which reveals a nonlinear mapping between the Gaussian field and the curvature perturbation.

We study the $1/c$ expansion of general relativity within a formulation that is compatible with both the Arnowitt-Deser-Misner and the Kol-Smolkin decompositions. The Einstein-Hilbert action takes a common form for those decompositions as they are dual to each other. We first develop a method to expand this generic form without choosing a particular slicing and then push the expansion up to $c^{-3}$ order within this novel approach. Next, we apply our technique to the Arnowitt-Deser-Misner decomposition and expand it up to $c^{-3}$ order explicitly. In order to demonstrate the applicability of our method and to highlight the duality at the level of expansion, we also perform the expansion in the Kol-Smolkin decomposition up to $c^{-1}$ order. Lastly, we make some all-order observations.

When 3D relative displacement $\mathbf{r}$ and velocity $\mathbf{v}$ between the pair in a gravitationally-bound system are precisely measured, the six measured quantities at one phase can allow elliptical orbit solutions at a given gravitational parameter $G$. Due to degeneracies between orbital-geometric parameters and $G$, individual Bayesian inferences and their statistical consolidation are needed to infer $G$ as recently suggested by a Bayesian 3D modeling algorithm. Here I present a fully general Bayesian algorithm suitable for wide binaries with two (almost) exact sky-projected relative positions (as in the Gaia data release 3) and the other four sufficiently precise quantities. Wide binaries meeting the requirements of the general algorithm to allow for its full potential are rare at present, largely because the measurement uncertainty of the line-of-sight (radial) separation is usually larger than the true separation. As a pilot study, the algorithm is applied to 32 Gaia binaries for which precise HARPS radial velocities are available. The value of $\Gamma \equiv \log_{10}\sqrt{G/G_{\rm N}}$ (where $G_{\rm N}$ is Newton's constant) is $-0.002_{-0.018}^{+0.012}$ supporting Newton for a combination of 24 binaries with Newtonian acceleration $g_{\rm N}>10^{-9}$m\,s$^{-2}$, while it is $\Gamma=0.134_{-0.036}^{+0.056}$ ($0.143_{-0.041}^{+0.068}$) for 8 (6) binaries with $g_{\rm N}<10^{-9}$ ($<10^{-9.5}$) m\,s$^{-2}$ representing $> 3.5\sigma$ discrepancy with Newton. However, one system (Stars HD189739 and HD189760) dominates the signal. Without it, the tension with Newton is significantly lessened with $\Gamma=0.063_{-0.041}^{+0.065}$. Thus, to verify the tentative signal, many such systems need to be discovered and their kinematic nature such as any possibility of hidden tertiary stars needs to be thoroughly addressed. The pilot study demonstrates the potential of the algorithm.

DESI observations of baryon acoustic oscillations (BAOs), combined with cosmic microwave background (CMB) and type-Ia supernova (SN Ia) data, suggest that the dark energy equation of state $w_{\rm DE}$ crosses the phantom divide from $w_{\rm DE} < -1$ to $w_{\rm DE} > -1$ at low redshifts. In shift-symmetric Horndeski and generalized Proca theories with luminal gravitational-wave speed and no direct couplings to dark matter, we show that such a phantom-divide crossing is generically difficult without theoretical pathologies. Breaking the shift symmetry in Horndeski theories allows this transition. We construct an explicit model with broken shift symmetry, in which the scalar field has a potential in addition to a Galileon self-interaction and a quadratic kinetic term. This model realizes the desired phantom-divide crossing at low redshifts without introducing ghosts and Laplacian instabilities.

Extreme-mass-ratio inspirals, in which a stellar-mass object orbits a supermassive black hole, are prime sources of millihertz gravitational waves for upcoming space-based detectors. While most studies assume idealized vacuum backgrounds, realistic extreme-mass-ratio binaries are embedded in astrophysical environments such as accretion disks, stellar clusters, or dark matter spikes, disks, and halos, which can significantly alter the orbital dynamics. We explore bound geodesics around general-relativistic solutions describing rotating black holes surrounded by matter halos for the first time, mapping how environmental effects interfere with the spacetime symmetries of vacuum spinning (Kerr) black holes. In particular, we find that the loss of a Carter-like constant leads to geodesic non-integrability and the onset of chaos. This manifests through the formation of resonant islands and chaotic layers around transient orbital resonances in phase space--features that are otherwise completely absent in integrable Kerr geodesics. Resonant islands, which are extended, non-zero volume regions in phase space, encapsulate periodic orbit points. Non-integrability dictates that all geodesics inside the resonant island share the periodicity of the resonance. Thus, the lifespan of resonances around non-Kerr objects can be significantly enhanced beyond the predicted lifetime of Kerr resonances. Consequently, these effects can leave distinct imprints on gravitational-wave signals, with significant implications for gravitational-wave modeling and parameter inference of astrophysical extreme-mass-ratio inspirals.

A particularly compelling aspect of the GW190521 event detected by the LIGO--Virgo--KAGRA (LVK) collaboration is that it has an extremely short duration, and lacks a clearly identifiable inspiral phase usually observed in the binary black holes (BBHs) coalescence. In this work, we hypothesize that GW190521 might represent a single, isolated gravitational wave (GW) echo pulse from the wormhole, which is the postmerger remnant of BBHs in another universe and connected to our universe through a throat. The ringdown signal after BBHs merged in another universe can pass through the throat of wormhole and be detected in our universe as a short-duration echo pulse. Our analysis results indicate that our model yields a network signal-to-noise ratio comparable to that of the standard BBHs merger model reported by the LVK collaboration. For GW190521, Bayesian model selection yields $\ln \mathcal{B}^{\text{Echo}}_{\text{BBH}} \simeq -2.9$, indicating that the data favor the BBH hypothesis over our echo-for-wormhole model.

The gradients act as invisible engines of transport, converting microscopic imbalances into macroscopic flows, and thus providing deep insights into the dynamics of physical systems. Thermal gradients do not merely drive the flow of heat, but they also set the microscopic constituents of the system into motion. In such scenarios, the constituents of the system not only transport energy but also diffuse collectively under the influence of these gradients. For the very first time, we present a first-principles investigation of the Soret and Dufour effects in hot and dense quantum chromodynamics (QCD) matter. We use the relativistic Boltzmann transport equation under the relaxation time approximation. By incorporating chemical potential and temperature gradients into the kinetic theory framework, we derive explicit expressions for the Dufour coefficient, which quantifies the heat flow due to concentration gradients, and the Soret coefficient, which describes the particle diffusion induced by thermal gradients. These coupled-transport phenomena are traditionally studied in multi-component classical systems at low energy scales. In this study, we follow quasiparticle models for the deconfined phase and the hadron resonance gas model for the confined hadronic phase in the context of heavy-ion collisions. This study provides novel insights into the thermo-diffusion and diffusion-thermo phenomena and opens avenues for incorporating such effects in hydrodynamic modeling and transport simulations of QCD matter.

We investigate the development of tearing-mode instability using the highest-resolution two-dimensional magnetohydrodynamic simulations of reconnecting current sheets performed on a uniform grid, for Lundquist numbers of $10^3 \le S \le 5 \times 10^5$ , reaching up to $65,536^2$ grid cells. We demonstrate a Sweet--Parker scaling of the reconnection rate $V_{\text{rec}} \sim S^{-1/2}$ up to Lundquist numbers $S \sim 10^4$. For larger values of Lundquist number, between $2\times 10^4\le S \le 2 \times 10^5$, plasmoid formation sets in, leading to a slight enhancement of the reconnection rate, $V_{\text{rec}} \sim S^{-1/3}$, consistent with the prediction from linear tearing mode induced reconnection, indicating that reconnection remains resistivity-dependent and therefore slow. In this range of $S$-values, the plasmoids do not undergo a merger cascade, as they are rapidly advected out of the reconnection layer. Only for $S > 2 \times 10^5$, we observe the nonlinear development of the tearing-mode instability, with plasmoid coalescence and a saturation of the reconnection rate at $V_\text{rec} / V_A \sim 0.01$. At such high $S$, however, the corresponding Reynolds number is large, reaching $\text{Re} > 2000$ even on scales comparable to the current-sheet thickness. We therefore conclude that, in astrophysical systems, it is essential to account for the dominant influence of turbulence and three-dimensional effects in the reconnection process.

Two body tunneling problems are hard to treat analytically due to the incompatibility between tunneling and perturbation theory. The lack of classical solutions of the Euclidean Lagrangian of continuous systems further thwarts semi-classical expansions. To develop an analytic theory which provides insight on interacting two-particle tunneling, we use new results to derive the Bethe-Salpeter equation of a tunneling field theory with Yukawa coupling. We show that in the one plus one dimensional case a closed form solution in the instantaneous positive-energy regime is permitted. We then compute the scattering amplitude by perturbing on interparticle interaction and recover the Lippmann-Schwinger equation to confirm physical consistency and relevancy.

Although the axion is the most compelling solution to the strong CP problem, the ad hoc introduced global Peccei-Quinn symmetry suffers from a severe fine-tuning problem known as the quality problem. In this Letter, we show that the discrete gauge symmetry $\mathbb Z_4 \times \mathbb Z_3$ motivated from the internal structure of the Standard Model can naturally predict a high-quality axion, leading to a distinct and testable parameter space. Remarkably, this minimal framework simultaneously accounts for neutrino masses, baryon asymmetry, and dark matter.

Cosmic inflation is the leading theory to explain early Universe history and structure formation. Non-oscillatory inflation is a class of models which can naturally introduce a post-inflationary stiff period of the Universe's evolution which boosts the signal of primordial gravitational waves (GWs), making it possible to observe them in forthcoming GW experiments. However, this pushes the GW energy density high enough to destabilise the process of Big Bang Nucleosynthesis (BBN). This problem can be overcome by "softening" the stiff period, so that the field is gradually tending towards freefall from a frozen start. Here, we consider a modified hybrid inflation model where the stiff period is driven by the waterfall field, allowing the barotropic parameter of the Universe to vary, so that it does not violate the BBN constraint but produces a characteristic gravitational wave spectrum soon to be observable.

We show that a bound impurity in a Bose-Einstein condensate can be directly mapped to an Unruh-DeWitt detector interacting with a relativistic quantum field. We provide explicit experimental parameters for an implementation using ${}^{39}\text{K}$ impurities coupled to a ${}^{87}\text{Rb}$ condensate via finite-time Feshbach tuning. As an application, we study the extraction of vacuum entanglement from distant regions of the condensate and find viable parameters for the implementation of entanglement harvesting.

We develop a current-based construction of generalized symmetries in $(3+1)$D twisted $BF$ topological quantum field theories (TQFTs), focusing on intrinsically non-invertible higher-form symmetries and their mixed anomalies. Starting from the equations of motion, we extract conserved currents and exponentiate the corresponding charges to obtain topological symmetry operators. This gives a step-by-step procedure for constructing symmetry operators, fusion, and anomaly diagnostics directly from the continuum action. We focus on twisted $BF$ theories with gauge group $G=\prod_i \mathbb{Z}_{N_i}$ and an $a\wedge a\wedge b$ twist, where $a$'s and $b$ are 1-form and 2-form gauge fields, respectively. These theories realize non-Abelian $(3+1)$D TQFTs supporting Borromean-rings braiding and describe three-dimensional non-Abelian topological orders in condensed matter. For $G=(\mathbb{Z}_2)^3$, a microscopic realization is given by the $\mathbb{D}_4$ Kitaev quantum double model. Two distinct classes of conserved currents emerge: Type-I currents generate invertible higher-form symmetries with group-like fusion, while Type-II currents require additional consistency conditions on gauge-field configurations, leading to intrinsically non-invertible symmetries dressed by projectors. We compute the fusion algebra: invertible operators admit inverses, while non-invertible ones exhibit multi-channel fusion governed by projector fusion. We diagnose mixed anomalies by coupling multiple conserved currents to background gauge fields, revealing two outcomes: anomalies canceled by anomaly inflow from a higher-dimensional theory, and intrinsic gauging obstructions encoded in the $(3+1)$D continuum theory. Overall, our results provide a unified and practical approach for constructing and characterizing higher-form symmetries, which can be extended to more general TQFTs and topological orders.

For simple Lie algebras we construct characteristic identities for split (polarized) Casimir operators in representations $T \otimes Y_n$ and $T \otimes Y_n'$, where $T$ -- defining (minimal fundamental for exceptional Lie algebras) representation, $Y_n$ -- n-Cartan powers of the adjoint representations $ad = Y_1$ and Y_n' -- special representations appeared in the Clebsch-Gordan decomposition of symmetric part of $ad^{\otimes n}$. By means of these characteristic identities, we derive (for all simple Lie algebras, except $\mathfrak{e}_8$) explicit formulae for invariant projectors onto irreducible subrepresentations arose in the decomposition of $T \otimes Y_n$. These projectors and characteristic identities are written in the universal form for all simple Lie algebras (except $\mathfrak{e}_8$) in terms of Vogel parameters. Universal formulas for the dimensions of the Casimir subrepresentations appeared in the decompositions of $T \otimes Y_n$ where found.

I describe my activities in Flavour Physics from 1976 to 2026. However, this 50th anniversary is not the only motivation for this writing. The second reason is the 350th anniversary of the discovery of the first animalcula by van Leeuvanhoek in 1676. Flavour physics makes it possible to search for new animalcula at distance scales far shorter than those resolved by van Leeuwenhoek in 1676 and even shorter than those directly accessible at the Large Hadron Collider. Achieving this goal requires not only precise measurements of a wide variety of processes, but also equally precise theoretical calculations, both within the Standard Model (SM) and beyond it. In this respect, next-to-leading-order (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations of various Wilson coefficients in the SM and beyond it, in which I was involved for two decades, as well as reliable treatments of non-perturbative QCD effects, are indispensable. Equally important is the proper choice of observables that are best suited to revealing these new animalcula of particle physics. Moreover, in my view it is crucial to develop strategies for the search for New Physics (NP) that go beyond the global fits that are very popular today. While effective field theories such as WET and SMEFT are formulated in terms of Wilson coefficients of the relevant operators, with correlations characteristic of the SM and of specific NP scenarios, the most direct tests of the SM and its extensions are, in my opinion, correlations among different observables that are characteristic of particular new animalcula at work. Numerous colourful plots in this article illustrate this point. I hope that these ideas are clearly conveyed in my Flavour Autobiography, which also includes my memories of many conferences, workshops, and schools, as well as related anecdotes that are not always directly connected to physics.

This paper investigates the influence of extra dimensions on the nature of the arrow of time. We demonstrate that the observed arrow of time can be explained by the monotonic growth of the multidimensional manifold's volume. Unlike traditional cosmological approaches based on the entropy of matter or radiation, our model identifies the primary temporal direction with the Bekenstein-Hawking-Wald entropy of the geometric background. By establishing a formal relation between the statistical weight of the multidimensional manifold and the multiplicity of causally disconnected regions, we reveal that time's directionality is driven by dominant entropy production in the higher-dimensional bulk. A key consequence of this approach is that the arrow of time remains a persistent feature for a 4D observer even in the vacuum limit. This global geometric evolution suppresses local statistical fluctuations and ensures a robust and stable entropy flow throughout the manifold.