We compute holographic timelike entanglement entropy for quantum BTZ black holes in a Karch-Randall braneworld scenario. These black holes are exact solutions of massive 3d gravity on the brane and are conjectured to be dual to thermal states in 2d defect CFTs, living at the interface of the brane and the boundary of the bulk $AdS_4$. Our analysis reveals an interesting relation between the tEE and the central charge pertaining to the dual CFT, which receives nontrivial corrections due to quantum backreaction effects on the Karch-Randall brane, which is explored non-perturbatively.

We construct an ultraviolet-complete, local, and unitary quantum field theory in 2+1 dimensions that exhibits spontaneous breaking of space-time parity, persisting to arbitrarily high temperatures. The theory is defined by a renormalization group trajectory, triggered by a relevant deformation of a conformal field theory, consisting of a critical biconical vector model and a free massless Dirac fermion. This deformation couples the fermion to the scalar sector, generating a renormalization group flow that terminates at a nontrivial infrared fixed point described by a conformal Gross-Neveu-Yukawa model and a decoupled critical vector model. By construction, the quantum field theory is parity invariant at zero temperature. However, we show that at sufficiently high temperatures, parity symmetry is spontaneously broken and remains so even in the infinite-temperature limit. Our analysis relies on both, perturbative renormalization group techniques in $4\!-\!\epsilon$ dimensions and functional renormalization group techniques directly in 2+1 dimensions.

We study the resurgent structure of the topological string dual to 2d $U(N)$ Yang-Mills on torus. We find closed form formulas for instanton amplitudes up to arbitrarily high instanton orders, based on which we propose the non-perturbative partition function including contributions from all the real instantons, which is real for positive modulus and string coupling. We also explore complex instantons and find two infinite towers of them. We expect them to correspond to BPS states in type II string.

Conformal field theory (CFT) can be placed on disparate space-time manifolds to facilitate investigations of their properties. For (2+1)D theories, one useful choice is the real projective space $\mathbb{RP}^3$ obtained by identifying antipodal points on the boundary sphere of a three-dimensional ball. One-point functions of scalar primary fields on this manifold generally do not vanish and encode the so-called crosscap coefficients. These coefficients also manifest on the sphere as the overlaps between certain crosscap states and CFT primary states. Taking the (2+1)D Ising CFT as a concrete example, we demonstrate that crosscap coefficients can be extracted from microscopic models. We construct crosscap states in both lattice models defined on polyhedrons and continuum models in Landau levels, where the degrees of freedom at antipodal points are entangled in Bell-type states. By computing their overlaps with the eigenstates of many-body Hamiltonians, we obtain results consistent with those from conformal bootstrap. Importantly, our approach directly reveals the absolute values of crosscap overlaps, whereas bootstrap calculations typically yield only their ratios. Furthermore, we investigate the finite-size scaling of these overlaps and their evolution under perturbations away from criticality.

We develop the holographic framework for the $\TTbar$ deformation of two-dimensional conformal field theories (CFT$_2$) with gravitational anomalies, characterized by unequal left and right central charges and holographically dual to topological massive gravity (TMG). Utilizing the mixed boundary condition prescription, we construct the deformed BTZ black hole geometry and derive the corresponding deformed energy spectrum, confirming that the universal flow equation remains valid despite the presence of gravitational anomalies. From the boundary perspective, we compute leading-order corrections to entanglement entropy and reflected entropy induced by the $\TTbar$ deformation, as well as the balanced partial entanglement entropy non-perturbatively. On the gravity side, these quantities are evaluated using spinning worldlines in the deformed bulk geometry, with results matching their field-theoretic counterparts in the high-temperature limit. We further analyze the reality condition for holographic entanglement entropy, which constrains the deformation parameter and reveals a generalized Hagedorn behavior. This Hagedorn-like transition is also independently reproduced from the asymptotic density of states in the deformed anomalous CFT$_2$, providing additional evidence for its universality.

We discuss free differential algebras (FDA's), a generalization of the Cartan-Maurer equations for the group manifold vielbein, appropriate for theories containing $p$-forms ($p >1$). Their dual formulation is an extension of Lie algebras, called $L_\infty$ algebras, and we illustrate this duality in a simple example. Finally we review the FDA structure and the dual $L_\infty$ structure of $d=11$ supergravity.

We give a review on hyperbolic magnetic monopoles and hyperbolic vortices obtained in the unified way through the conformal equivalence by the dimensional reduction from the symmetric instantons with various spatial symmetries in the four-dimensional Euclidean Yang-Mills theory. They are used to understand quark confinement in the sense of the area law of the Wilson loop average in a semi-classical picture from a unified treatment of Atiyah's hyperbolic magnetic monopole and Witten-Manton's hyperbolic vortex. In this way quark confinement is shown to be realized by the the non-perturbative vacuum disordered by these topological defects. For this purpose we start from the 4-dim. Euclidean Yang-Mills theory and require the conformal equivalence between the 4-dim. Euclidean space and the possible curved spacetimes with some compact dimensions. This requirement forces us to restrict the gauge configurations of this http URL-Mills instantons to those with some spatial symmetries (called symmetric instantons) which are identified with magnetic monopoles and vortices living in the lower-dimensional curved hyperbolic spacetime with constant negative curvature through the dimensional reduction. At the same time, this scheme caused by the dimensional reduction give a holographic description of hyperbolic magnetic monopole dominance on AdS3 in the rigorous way without any further assumptions, which does not hold in the flat Euclidean case. This unified treatment of two topological defects is shown to give the semi-classical picture for quark confinement in the sense of Wilson. We give the understanding of the result from the viewpoint of the gauge-covariant Cho-Duan-Ge-Faddeev-Niemi decomposition for the gauge field.

The renormalization group flow of the multiscalar interacting $\varphi^3$ theory in $d=6$ dimensions is known to have a gradient structure, in which suitable generalizations of the beta functions $B^{I}$ emerge as the gradient of a scalar function $A$, $\partial_I A = T_{IJ} B^J $, with a nontrivial tensor $T_{IJ}$ in the space of couplings. This has been shown directly to three loops in schemes such as $\overline{\rm MS}$ and can be argued in general by identifying $A$ with the coefficient of the topological term of the trace-anomaly in $d=6$ up to a normalization. In this paper we show that the same renormalization group has a gradient structure in $d=6-\varepsilon$. The requirement of a gradient structure is translated to linear constraints that the coefficients of the $\overline{\rm MS}$ beta functions must obey, one of which is new and pertinent only to the extension to $d \neq 6$.

We present a new mass generation mechanism for linearized gravity in three spacetime dimensions, which consists of a lower-dimensional Chern-Simons-like term added to the invariant action. The propagators of the gauge fixed massive action show a massive pole and a good massless limit. Moreover, we show that, as the Topological Massive Gravity model of Deser, Jackiw and Templeton, this theory displays one propagating massive DoF, which can be traced back to the transverse part of the spatial Ricci tensor. Finally, the action of this linearized massive gravity is characterized by an algebraic structure formed by a set of Ward operators, which uniquely determine the theory.

In this work, we present a recurrence relation for the instanton partition function of $\mathcal{N}=2$ SYM $SU(N)$ gauge theory with $2N$ fundamental multiplets. The main difficulty lies in determining the asymptotic behaviour of the partition function in the regime of large vacuum expectation values of the Higgs field. We demonstrate that, in this limit, the partition function is governed by the Quantum Seiberg-Witten curves, as it is in the Nekrasov-Shatashvili limit, up to a normalisation constant. With the found asymptotic behaviour, we are able to write the recurrence relation for the partition function and to find the effective infrared coupling constant. The resulting effective constant is an inverse to a modular function with respect to a certain triangle group, and the asymptotic itself is a product of modular functions and forms with respect to the same group.

We formulate a discrete model of holography on biregular trees, which are discrete symmetric spaces associated with the bulk isometry group SU(3) over the unramified quadratic extension of a nonarchimedean field. For a scalar field theory on biregular trees, the bulk-to-bulk and bulk-to-boundary propagators exhibit distinct features absent on the regular tree or continuum AdS spaces, arising from the semihomogeneous nature of the bulk space. We compute the two- and three-point correlators of the putative boundary dual. The three-point correlator exhibits a nontrivial "tensor structure" via dependence on the homogeneity degree of a unique bulk point specified in terms of boundary insertion points. The computed OPE coefficients show dependence on zeta functions associated with the unramified quadratic extension of a nonarchimedean field. This work initiates the formulation of holography on a family of discrete holographic spaces that exhibit features of both flat space and negatively curved space.

6d supergravities with non-abelian gauge group are subject to many consistency conditions. While the absence of local gauge and gravitational anomalies allows for infinitely many models, we show that those conditions stemming from the absence of both local and global anomalies together are strong enough to leave only finitely many consistent models. To do this we distill the consequences of anomaly cancellation into a high-dimensional linear program whose dual can be efficiently studied using standard techniques. We obtain a universal bound on the number of tensor multiplets $T \leq 11 \cdot 273 = 3003$ and show that this leads to a finite landscape of consistent non-abelian models. Interestingly, the model which saturates this bound has gauge group $[E_8 \times F_4 \times (G_2 \times \mathrm{SU}(2))^2]^{273}$, which bears a striking resemblance to the model which saturates the bound $T \leq 193$ for F-theory constructions.

We propose a construction of fiducial observers in the throat region of near-extremal black holes within the framework of JT quantum gravity, leading to a notion of local observers in a highly quantum regime of the gravitational field. The construction is based on an earlier proposal for light-ray anchoring to the asymptotic boundary and is uniquely fixed at the semiclassical level by demanding that the notion of time translations for an observer at the asymptotic boundary of JT gravity should be extended into the bulk as the flow of a conformal isometry. Since conformal isometries are a necessary condition for geometric modular flow, our construction is amenable as a candidate geometric gravitational dressing that may be interpreted via the modular crossed product, potentially connecting our choice of dressing with recent developments on the literature on local observables in quantum gravity. Taking this definition beyond the semiclassical regime, we compute quantum gravitational wormhole contributions to the black hole thermal atmosphere, directly producing a finite thermal entropy and leading to a quantum description of the stretched horizon in this model.

We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$ in the confining phase of the theory in the infinite $N$ limit. By leveraging the symmetries of these models and using non-linear relaxation, we consider constraints up to level 14, e.g., constraints from traces of words of length $\le 14$. Our results are more precise than large $N$, continuum extrapolations of lattice Monte Carlo simulations, including an estimate of certain simple observables up to 8 significant digits.

In order to derive model-independent observational bounds on dark energy/modified gravity theories, a typical approach is to constrain parametrised models intended to capture the space of dark energy theories. Here we investigate in detail the effect that the nature of these parametrisations can have, finding significant effects on the resulting cosmological dark energy constraints. In order to observationally distinguish well-motivated and physical parametrisations from unphysical ones, it is crucial to understand the theoretical priors that physical parametrisations place on the phenomenology of dark energy. To this end we discuss a range of theoretical priors that can be imposed on general dark energy parametrisations, and their effect on the constraints on the phenomenology of dynamical dark energy. More specifically, we investigate both the phenomenological $\{\mu,\Sigma\}$ parametrisation as well as effective field theory (EFT) inspired approaches to model dark energy interactions. We compare the constraints obtained in both approaches for different phenomenological and theory-informed time-dependences for the underlying functional degrees of freedom, discuss the effects of priors derived from gravitational wave physics, and investigate the interplay between constraints on parameters constraining only the background evolution vs. parameters controlling linear perturbations.

Gauge theories compose a large class of interacting conformal field theories in 3d, among which an outstanding category is critical Chern-Simons-matter theories. In this paper, we focus on one of the simplest instances: one complex critical scalar coupled to $\mathrm{U}(1)_2$ Chern-Simons gauge field. It is theoretically interesting as it is conjectured to exhibit dualities between four simple Lagrangian descriptions, but also practically important as it describes the transition between Kalmeyer-Laughlin chiral spin liquid (or $\nu=1/2$ bosonic Laughlin state) and trivially gapped phase. Using the fuzzy sphere regularisation, we realise this theory as a transition on the spherical lowest Landau level between a $\nu_f=2$ fermionic integer quantum Hall state and a $\nu_b=1/2$ bosonic fractional quantum Hall state. We show that this transition is continuous and has emergent conformal symmetry. By studying the operator spectrum, we show that there exists only one relevant singlet with scaling dimension $\Delta_S=1.52(18)$. We also discuss other higher operators and the consequences of our results.

We present a novel approach for constructing quasi-isospectral higher-order Hamiltonians from time-independent Lax pairs by reversing the conventional interpretation of the Lax pair operators. Instead of treating the typically second-order $L$-operator as the Hamiltonian, we take the higher-order $M$-operator as the starting point and construct a sequence of quasi-isospectral operators via intertwining techniques. This procedure yields a variety of new higher-order Hamiltonians that are isospectral to each other, except for at least one state. We illustrate the approach with explicit examples derived from the KdV equation and its extensions, discussing the properties of the resulting operators based on rational, hyperbolic, and elliptic function solutions. In some cases, we present infinite sequences of quasi-isospectral Hamiltonians, which we generalise to shape-invariant differential operators capable of generating such sequences. Our framework provides a systematic mechanism for generating new integrable systems from known Lax pairs.

We investigate the cosmological dynamics of scalar fields governed by higher-order gravity, with particular emphasis on models inspired by the Pais-Uhlenbeck oscillator--a prototypical fourth-order system known for its connection to ghost-free formulations. By recasting the field equations into a slow-fast dynamical system, we analyze phase space evolution across exponential and power-law coupling regimes. Our approach integrates numerical simulations and geometric methods to visualize trajectories, stream flows, and asymptotic behavior under varying potential parameters. The underlying system admits singular surfaces and non-smooth transitions, revealing intricate dynamical structures. We examine the stability of de Sitter solutions, the crossing of the phantom divide, and the emergence of cyclic behavior through multiple-scale analysis. The inclusion of radiation and dust fluids enables the creation of realistic cosmological scenarios, including a transient matter-dominated era and a late-time accelerated expansion. Our results highlight the viability of Pais-Uhlenbeck scalar models in accounting for inflationary dynamics and dark energy, offering diagnostic tools for characterizing attractors and bifurcation phenomena in higher-derivative cosmology.

In this work, we study the electromagnetic energy and energy rate spectra produced by a point particle in the presence of plane wave fields. Our approach is based on a semiclassical formulation, in which the current distribution that generates electromagnetic radiation is treated classically while the radiation field is quantum. Unlike the classical energy spectrum--which exhibits divergences linked to the duration of interaction between the particle and the external field--the semiclassical spectrum is finite because radiation is produced during the quantum transition from an initial state without photons to the final state with photons at time $t$. In our formulation, we find that the maximum energy spectrum emitted by the particle is linearly proportional to time or phase, depending on the external field. This allowed us not only to extract the maximum energy rate spectra emitted by the particle but also to correlate them with energy rates derived in the framework of Classical Electrodynamics and Quantum Electrodynamics.

In this study, the methodology proposed by Goon and Penco for investigating the universality on thermodynamic relations with corrections in de Sitter black holes is extended. A universal thermodynamic extremality relation, under consideration of the mass of the spacetime $M$ with various state parameters, proposed by Goon and Penco is investigated in higher dimensional spacetime, the established universal conclusions are not impacted by the convergence of energy from the coexistence region of two horizons to the point $N$ or $C$. Furthermore, by incorporating the shift of the angular momentum into our analysis, a more universal relation is derived, specifically applicable to rotating configurations. Notably, a novel conjecture is formulated that establishes a universal relationship framework connecting shifted thermodynamic quantities across arbitrary black hole backgrounds. These findings are expected to offer profound insights into the fundamental principles of quantum gravity.

We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible discretization of the parameter space, we incorporate both group cochains and parameter-space differentials, enabling the systematic construction of equivariant topological invariants. We derive a fixed-point formula for the higher Berry invariant in the case where the symmetry action has isolated fixed points. This reveals that the phase transition point between Haldane and trivial phases acts as a monopole-like defect where higher Berry curvature emanates. We further discuss hierarchical structures of topological defects in the parameter space, governed by symmetry reductions and compatibility with subgroup structures.

We investigate the quantum behavior of a charm-anticharm bound system under the influence of a magnetic field within the symplectic formulation of Quantum Mechanics. Employing a perturbative approach, we obtain the ground and first excited states of the system described by the Cornell potential, which incorporates both confining and nonconfining interactions. After perfoming a Bohlin mapping in phase space, we solve the time-independent symplectic Pauli-Schrödinger-type equation and determine the corresponding Wigner function. Special attention is given to the observation of the confinement of the quark-antiquark (meson $c\overline{c}$) that is revealed in the phase space structure. And the introduction of spin effect (external magnetic field) in modifying the quantum characteristics of the system. Our results reveal that the magnetic enhances the negativity of the Wigner function, signaling stronger quantum interference and a departure from classical behavior. The negativity thus serve as a quantitative measure of the system's non-classicality. In addition we have computed the mass spectra of the $c\overline{c}$ meson and present result are in agreement with experimental data, improving previous theoretical studies.

We investigate the twisted Eguchi-Kawai (TEK) reduced model of four-dimensional $SU(N)$ gauge theory in the presence of two-flavor adjoint fermions (adjoint TEK model). Using Monte Carlo simulations with $N=121$, twist parameter $k=1$, hopping parameter $\kappa=0.01$-$0.03$ ($\ll\kappa_c $) and inverse 't Hooft coupling $b=0.30$-$0.45$, we show that heavy adjoint fermions stabilize the $(\mathbb{Z}_N)^4$ center-symmetric vacuum even for the minimal twist satisfying $k/\sqrt{N} < 1/9$, where the $(\mathbb{Z}_N)^4$ symmetry is spontaneously broken in the absence of adjoint fermions. This result also suggests that the adjoint TEK model with the minimal twist is equivalent to $SU(N)$ gauge theory over a broader $(\kappa,b)$ parameter region than the adjoint EK model without twist. We further extend our analysis to a partially reduced model to realize a geometry akin to $\mathbb{R}^3 \times S^1$ and study the theory under $S^1$ compactification with periodic adjoint fermions. Numerical simulations with $N=16$-$49$, $b=0.30$-$0.46$ and $\kappa=0.03$-$0.16$ supports the adiabatic continuity conjecture: with periodic adjoint fermions, the theory remains in a center-symmetric (confined) phase as the $S^1$ circle size is reduced, in contrast to the deconfining transition observed in the pure TEK model or in the TEK model with antiperiodic adjoint fermions. We present the Polyakov loop measurements and consistency checks supporting these findings.

The gauge field theory of the standard electroweak model in the presence of the electroweak bubble wall is investigated, with an eye toward its applications to microscopic phenomena which are supposed to have occurred during the phase transition in the early universe. The asymptotic fields are defined anew so that the effects of the position-dependent Higgs condensate are taken into account through the position-dependent $W$ and $Z$ boson masses. A novel method of massive gauge field quantization in the $R_{\xi}$-gauge with $\xi =1$ is proposed for the case of the position-dependent masses. Our method is based on the eigenfunction expansion method associated with second-order differential operators, i.e., a sort of generalized Fourier this http URL commutation relations of creation and annihilation operators of various wave propagation modes are given in terms of the so-called spectral function. The decoupling of unphysical states from the physical S-matrix is also investigated along the line of Kugo-Ojima's quartet mechanism on the basis of the BRST symmetry. It is pointed out that one of the quartet fields is not merely the unphysical scalar field but should be a linear combination of the unphysical scalar and the gauge fields. The physical and unphysical polarizations of the gauge field waves are unambiguously distinguished and this will help us evaluate the friction caused by the physical polarization states of $W$ and $Z$ boson waves on the bubble wall during the phase transition in the early universe.

In this work, we tested the thermal behavior of a class of regular black hole solutions defined as generalized black-bounce spacetimes. We introduce several novel configurations governed by different mass functions and geometric deformations, illustrated by parameters controlling regularity and horizon structure. Using the Hamilton Jacobi tunneling method, we compute the Hawking temperature associated with each model and analyze its dependence on the underlying parameters. We find that all proposed geometries are free of curvature singularities and exhibit positive, well defined quasi-local masses in the Hernandez Misner Sharp formalism. Also, we demonstrate that these models may possess multiple horizons, including extremal and asymmetric cases, while typically violating classical energy conditions in the vicinity of the bounce. Our results show and illustrate the structure and thermodynamic stability of these regular solutions.

Using the latest observational data, we constrain the inflationary dynamics and the subsequent reheating epoch. Predictions for both phases can be significantly improved by employing numerically computed results compared to the slow-roll approximations. These results enable a more accurate reassessment of the observational viability of inflationary models, provide tighter constraints on the reheating history, and help lift the degeneracies in the predictions of inflation and reheating dynamics. Given current observational bounds, this enables a more accurate understanding of the early universe physics.

Supernovae (SNe) associated with X-Ray Flashes (XRFs) are extremely rare. Therefore, the discovery of each new object in this class offers a unique opportunity to improve our understanding about their origins and potential connection with other high-energy phenomena. SN 2025kg is one of the most recent events discovered in this category, and exhibits a double-peaked light curve, with an initial cooling phase followed by the main peak. Here, we investigate the possible mechanisms powering its bolometric light curve and expansion velocities, using numerical calculations to simulate the explosion. We found that low ejecta masses (Mej ~ 2 Msun) and moderate explosion energies (E ~ 2e51 erg) are required to reproduce the data. Our models also show that a large amount of nickel (M_Ni = 0.85 Msun) is needed to achieve the high luminosity of SN 2025kg, which makes this scenario difficult to sustain. As an alternative, we explore a model in which a millisecond magnetar serves as the primary energy source. A magnetar with a spin period of 3 ms, approximately, and a magnetic field of 28e14 G gives an adequate match to the data. To account for the early cooling phase, we assume the presence of a dense circumstellar material surrounding the progenitor, with a mass of 0.27 Msun and an extension of 500 Rsun. A comparison and modeling of a select group of SNe--SN 2006aj, SN 2020bvc and SN 2023pel--is also presented. A remarkable similarity emerges between SN 2025kg and SN 2023pel. As SN 2023pel was recently proposed to be powered by a magnetar, this further supports the magnetar scenario for SN 2025kg.

In this paper, we examine the scaling laws in gravitational system from the perspective of free energy landscape. It has been found that for some special black holes, their critical exponents are beyond mean field theory, and more surprisingly violate the scaling laws. We find that the main reason for the violation of the scaling laws is that the heat capacity at constant volume for these black holes is 0, so the critical exponent $\alpha$ is often treated as 0 and can not be derived from the scaling hypothesis while another three critical exponents can. We also find that the strange critical exponents means there is a symmetry violation in the order parameter.

We study a free open fermionic string theory within a non-commutative target phase-space, considering non-commutativity in both the spatial and momentum components. The altered commutation relations are expressed in terms of mode oscillators. We derive modified super-Virasoro algebras for both the Ramond and Neveu-Schwarz sectors, which include new anomaly terms arising from non-commutativity. This non-commutativity breaks Lorentz covariance and leads to a non-diagonal mass operator in the conventional Fock space. To address this, we propose a redefinition of the Fock space that diagonalizes the matrices of non-commutativity parameters, thereby yielding a diagonal mass operator. To eliminate the anomalies in the Virasoro algebra caused by non-commutativity and recover the standard mass spectrum, certain constraints are imposed on the non-commutativity parameters. Under these conditions, the GSO projection becomes viable, allowing for the emergence of space-time supersymmetry. Additional constraints on the zero modes of the non-commutativity parameters are introduced to restore Lorentz covariance.

We study twisted traces on the quantum Higgs branches $A_{\operatorname{Higgs}}$ of $3d, \mathcal{N}=4$ gauge theories, that is, the quantum Hamiltonian reductions of Weyl algebras. In theories which are good, we define a twisted trace that arises naturally from the correlation functions of the gauge theory. We show that this trace induces an inner product and a short star product on $A_{\operatorname{Higgs}}$. We analyze this trace in the case of an abelian gauge group and show that it has a natural expansion in terms of the twisted traces of Verma modules, confirming a conjecture of the first author and Okazaki. This expansion has a natural interpretation in terms of 3-d mirror symmetry, and we predict that it can be interpreted as an Atiyah-Bott fixed-point formula under the quantum Hikita isomorphism.

With the aim of investigating the existence of an integrable elliptic deformation of strings on $\mathsf{AdS}_3 \times \mathsf{S}^3 \times \mathsf{T}^4$, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on $\mathsf{AdS}_3 \times \mathsf{S}^3$ in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden $\mathsf{U}(1)$ symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed $\mathsf{AdS}_3 \times \mathsf{S}^3 \times \mathsf{T}^4$ light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

Motivated by recent study of DSSYK and the non-commutative nature of its bulk dual, we review and analyze an example of a non-commutative spacetime known as the quantum disk proposed by L. Vaksman. The quantum disk is defined as the space whose isometries are generated by the quantum algebra $U_q(\mathfrak{su}_{1,1})$. We review how this algebra is defined and its associated group $SU_q(1,1)$ that it generates, highlighting its non-trivial coproduct that sources bulk non-commutativity. We analyze the structure of holography on the quantum disk and study the imprint of non-commutativity on the putative boundary dual.

Finite-temperature one-loop renormalization of the Standard Model, coupled with dynamic metric, is conducted in this study. The entire analysis is coherently carried out by using the refined background field method, applied in the spirit of the Coleman-Weinberg technique. The general form of the propagator, introduced in our previous work to facilitate Feynman diagram computation in a general curved background, proves useful in the presence of time-dependent temperature. Its utilization allows for the renormalization analysis of a FLRW background to essentially reduce to that of a constant finite-T flat spacetime. For infrared physics, the actual curved background should be considered. The implications of our findings for cosmology, particularly the cosmological constant problem and Hubble tension, are discussed.

We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ Majorana fermions with $q$-body fermion interaction with $q=4,6,8$ for a range of sparse parameter $k$ that controls the number of remaining terms in the original SYK model after sparsification. The critical value of $k$ below which the model ceases to be holographic, denoted $k_c$, has been subject of several recent investigations. Using Krylov complexity as a probe, we find that the peak value of complexity does not change as we increase $k$ beyond $k \ge k_{\text{min}}$ at large temperatures. We argue that this behavior is related to the change in the holographic nature of the Hamiltonian in the sparse SYK-type models such that the model is holographic for all $k \ge k_{\text{min}} \approx k_c$. Our results provide a novel way to determine $k_c$ in SYK-type models.

We study the line defect half-indices of 3d $\mathcal{N}=2$ supersymmetric Chern-Simons (CS) theories with (special)unitary, symplectic, orthogonal and exceptional gauge groups. We find that they have several beautiful infinite product $q$-series expressions in terms of Ramanujan's general theta function. For the theories with fundamental chiral multiplets, the pairs of the Neumann half-indices and one-point functions of the fundamental Wilson lines form a basis for the line defect indices in terms of the Rogers-Ramanujan type functions. Furthermore, the theories with an adjoint chiral admit the expressions as the eta-products. In particular, for the $SU(N)_{-2N}$ CS theory, there is a one-to-one correspondence between the BPS boundary local operators and the $N$-core partitions.

Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field $\phi$ in $d$ dimensions coupled to a random source $h$ with quenched disorder. Despite the presence of a mass scale governing the disorder distribution, we derive a new description of the theory that allows us to show that the theory is gapless and invariant under conformal symmetry, which acts in a non-trivial way on $\phi$ and $h$. This manifest CFT description reveals the presence of exotic continuous symmetries, such as nilpotent bosonic ones, in the quenched theory. We also reconsider Cardy's CFT description defined through the replica trick. In this description, the nilpotent symmetries reveal a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit maps of correlation functions between such CFTs and the original quenched theory. The maps are non-trivial and show that conformal behaviour is manifest only when considering suitable linear combinations of averages of products of correlators. We also briefly discuss how familiar notions like normal ordering of composite operators and OPE can be generalized in the presence of the more complicated local observables in the quenched theory.

In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $\mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S=\mathbb{C}^*$ we recover the celebrated $Lw_{1+\infty}$ algebra. For the 2-sphere $S^2$, the wedge algebra reduces to a central extension of the anti-self-dual projection of the Poincaré algebra. We then extend $\mathcal{W}(S)$ outside of the wedge space and build a new Lie algebra $\mathcal{W}_\sigma(S)$, which can be viewed as a deformation of the wedge algebra by a spin two field $\sigma$ playing the role of the shear at a cut of $\mathscr{I}$. This algebra represents the gravitational symmetry algebra in the presence of a non trivial shear and is characterized by a covariantized version of the wedge condition. Finally, we construct a dressing map that provides a Lie algebra isomorphism between the covariant and regular wedge algebras.

In this paper we construct a non-perturbative action of the higher spin symmetry algebra on the gravitational phase space. We introduce a symmetry algebroid $\mathcal{T}$ which allows us to include radiation in an algebraic framework. We show that $\mathcal{T}$ admits a non-linear realization on the asymptotic phase space generated by a Noether charge defined non-perturbatively for all spins. Besides, this Noether charge is conserved in the absence of radiation. Moreover, at non radiative cuts, the algebroid can be restricted to the wedge symmetry algebra studied in arXiv:2409.12178. The key ingredient for our construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic Einstein's equations. This result then guarantees that the underlying symmetry algebra is also represented canonically.

We construct backreacted geometries dual to the supersymmetric mass deformation of the IKKT matrix model. They are Euclidean type IIB supergravity solutions given in terms of an electrostatic potential, having $SO(7)\times SO(3)$ isometry and 16 supersymmetries. Quantizing the fluxes, we find that the supergravity solutions are in one-to-one correspondence with fuzzy sphere vacua of the matrix model.

Using supersymmetric localization, we compute the partition function and some protected correlators of the polarized IKKT matrix model. Surprisingly, we find that the original IKKT model is different from polarized IKKT in the limit of vanishing mass deformation. We study different regimes of the localization results and recover the electrostatic problem which defines the gravity dual.

We prove that the generalised second law (GSL), with an appropriate modification, holds in perturbative gravity to all orders beyond the semiclassical limit and without a UV cutoff imposed on the fields. Our proof uses algebraic techniques and builds on the recent work of Faulkner and Speranza, which combined Wall's proof of the GSL with the identification of generalised entropy as the von Neumann entropy of a boost-invariant crossed product algebra. The key additional step in our approach is to further impose invariance under null translations. Doing so requires one to describe horizon exterior regions in a relational manner, so we introduce `dynamical cuts': quantum reference frames which give the location of a cut of the horizon. We use idealised dynamical cuts, but expect that our methods can be generalised to more realistic models. The modified GSL that we prove says that the difference in generalised entropies of the regions outside two dynamical cuts is bounded below by the free energy of the degrees of freedom giving the location of the later cut. If one takes a semiclassical limit, imposes a UV cutoff, and requires the cuts to obey certain energy conditions, then our result reduces to the standard GSL.

In this work, we present a new geometric transition in non-compact Calabi-Yau 4-folds, specifically for the cone over the 7d Sasaki-Einstein manifold $Q^{\scriptscriptstyle(1,1,1)}/\mathbb{Z}_{N}$. We discover a new smoothing of such Calabi-Yau 4-fold singularity via a partial resolution+deformation, which can be interpreted as a confined phase for a 3d $\mathcal{N}=2$ $SU(N)$ gauge theory. The confining strings are realized as M2-branes wrapping the torsional 1-cycles in this new geometric phase. We have also computed the generalized global symmetries, including finite $(-1)$-form symmetries, and SymTFT action using the link topology and intersection numbers of the resolved Calabi-Yau 4-fold.

We construct a non-perturbative action of the higher spin symmetry algebra on the asymptotic Yang-Mills phase space. We introduce a symmetry algebroid which admits a realization on the asymptotic phase space generated by a Noether charge defined non-perturbatively for all spins. This Noether charge is naturally conserved in the absence of radiation. Furthermore, the algebroid can be restricted to the covariant wedge symmetry algebra, which we analyze for non radiative cuts. The key ingredient in this construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic Yang-Mills equations of motion. This result then guarantees that the underlying symmetry algebra is represented canonically as well.

A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that emerge from bosonic abelian Chern-Simons theories, playing the role of a symmetry topological field theory, by imposing topological boundary conditions. Our construction includes the fermionic generalization of code CFTs. When the Chern-Simons theory is associated with the root lattice of a simply laced Lie algebra, this approach yields a fermionic CFT with a level-one affine Lie algebra symmetry. As an application, we consider the Chern-Simons theories corresponding to a class of supersymmetric vertex operator algebras studied by Johnson-Freyd and classify their fermionic topological boundary conditions that give rise to supersymmetric CFTs.

We study generalized scalar field models coupled to impurities in Minkowski spacetime with arbitrary dimensions. The investigation concerns a class of models that depends explicitly on the spacetime coordinates and also, it reveals the presence of a second-order tensor that can have null divergence if a first-order equation and a constraint are satisfied. We obtain the conditions to get compatibility between the equation of motion and the first-order equation, within a framework that is also used in the static case, to show that the introduction of an auxiliary function may allow to describe the energy density of the solution as a divergence. Stability of the solution under rescale of argument, translation in the space and small fluctuations are also fully investigated. We further illustrate the procedure considering the canonical model and also, the $k$-field and Born-Infeld-like models. The results show that stable solutions can be obtained in arbitrary dimensions, and the stability seems to be related to the first-order equation that emerges from imposing null divergence of the aforementioned tensor.

We revisited the equivalence between the second- and first-order formulations of the Yang-Mills (YM) and gravity using the path integral formalism. We demonstrated that structural identities can be derived to relate Green's functions of auxiliary fields, computed in the first-order formulation, to Green's functions of composite fields in the second-order formulation. In YM theory, these identities can be verified at the integrand level of the loop integrals. For gravity, the path integral was obtained through the Faddeev-Senjanović procedure. The Senjanović determinant plays a key role in canceling tadpole-like contributions, which vanish in the dimensional regularization scheme but persist at finite temperature. Thus, the equivalence between the two formalisms is maintained at finite temperature. We also studied the coupling to matter. In YM theory, we investigated both minimal and non-minimal couplings. We derived first-order formulations, equivalent to the respective second-order formulations, by employing a procedure that introduces Lagrange multipliers (LM). This procedure can be easily generalized to gravity. We also considered an alternative gravity model, which is both renormalizable and unitary, that uses LM to restrict the loop expansion to one-loop order. However, this approach leads to a doubling of one-loop contributions due to the additional degrees of freedom associated with Ostrogradsky instabilities. To address this, we proposed a modified formalism that resolves these issues by requiring the path integral to be invariant under field redefinitions. This introduces ghost fields responsible for canceling the extra one-loop contributions arising from the LM fields, while also removing unphysical degrees of freedom. We also demonstrated that the modified formalism and the Faddeev-Popov procedure commute, indicating that the LM can be viewed as purely quantum fields.

We investigate the dynamics of black hole critical collapse in the limit of a large number of spacetime dimensions, $D$. In particular, we study the spherical gravitational collapse of a massless, scale-invariant scalar field with continuous self-similarity (CSS). The large number of dimensions provides a natural separation of scales, simplifying the equations of motion at each scale where different effects dominate. With this approximation scheme, we construct matched asymptotic solutions for this family, including the critical solution. We then compute the mass critical exponent of the black hole for linear perturbations that break CSS, finding that it asymptotes to a constant value in infinite dimensions. Additionally, we present a link between these solutions and closed Friedmann--Lemaître--Robertson--Walker (FLRW) cosmologies with a dimension-dependent equation of state and cosmological constant. The critical solution corresponds to an unstable Einstein-like universe, while subcritical and supercritical solutions correspond to bouncing and crunching cosmologies respectively. Our results provide a proof of concept for the large-$D$ expansion as a powerful analytic tool in gravitational collapse and suggest potential extensions to other self-similar systems.

Using the $SO ({\cal N})$ superspace formulation for $\cal N$-extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the ${\cal N} =4$ case. The specific feature of this choice is that the so-called super Cotton tensor $X^{IJKL} = X^{[IJKL]}$, which exists for ${\cal N} \geq 4$, is equivalent to the scalar $X$ defined by $X^{IJKL} = \varepsilon^{IJKL} X$. This scalar may be used as a deformation parameter. In the family of $(p,q)$ anti-de Sitter (AdS) superspaces with $p+q=4$, it is known that $X\neq 0$ exists only if $p=4$ and $q=0$. In general, the $(4,0)$ AdS superspaces are characterised by the structure group $SL(2,{\mathbb R}) \times SO (4)$ and their geometry is determined by two constant parameters, $S$ and $X$, of which the former determines the AdS curvature, while the $R$-symmetry curvature is determined by the parameters $(X+2S)$ and $(X-2S)$ in the left and right sectors of $SU(2)_{\rm L} \times SU(2)_{\rm R}$, respectively. Setting $S=0$ leads to the so-called deformed ${\cal N}=4$ Minkowski superspace ${\mathbb M}^{3|8}_X$ introduced thirteen years ago. We construct general interacting supersymmetric field theories in ${\mathbb M}^{3|8}_X$ and demonstrate that they originate as massive deformations of the following two families of ${\cal N} =4$ theories in standard Minkowski superspace ${\mathbb M}^{3|8}$: (i) ${\cal N}=4$ superconformal field theories; and (ii) ${\cal N}=4$ supersymmetric gauge theories in ${\mathbb M}^{3|8}$ which are not superconformal but possess the $R$-symmetry group $SU(2)_{\rm L} \times SU(2)_{\rm R}$. Extensions of the theories in (ii) to ${\mathbb M}^{3|8}_X$ necessarily contain Chern-Simons terms at the component level. We also demonstrate the generation of topologically massive ${\cal N}=4$ supersymmetric gauge theories from radiative corrections in the hypermultiplet sector.

We generalize the analysis of the asymptotic higher spin symmetries developed in the first three parts of this series by considering the minimal coupling of Einstein Gravity and Yang-Mills theory. We show that there exist symmetry parameters that satisfy a collection of dual equations of motion, which allow the construction of an infinite collection of charges that are conserved in the absence of radiation. These Noether charges act on the Einstein Yang-Mills phase space canonically and non-linearly. Their action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts and generalizes the celestial $sw_{1+\infty}$ algebra. The corresponding symmetry bracket is shown to satisfy the Jacobi identity and an interesting cross-product structure, which is analyzed in details.

Previously, we showed that massless scalar point particles cannot propagate on classical backgrounds of chiral higher-spin theory. This conclusion was derived from the analysis of the light-cone consistency conditions occurring at the second order in interactions. In the present paper, we extend this result to the case of massive particles, showing that these cannot propagate on chiral higher-spin backgrounds either. In order to do that, we use a different and more direct approach, which does not rely on special simplifications occurring for massless particles. Namely, we solve the light-cone consistency conditions at the given order in complete generality and then show that all the Hamiltonians found are inevitably non-local. We emphasise connections between the resulting procedure and the on-shell methods applied to worldline scattering observables.

We study the Type IIB eight-derivative effective Lagrangian beyond the quartic level, focusing on interactions involving gravitons and axio-dilatons. We show how to translate five-point scattering amplitudes into genuine five-point contact terms and extract all perturbative contributions to the effective action. Our result is consistent with T-duality predictions at tree level in the NSNS sector. We find that couplings with an even/odd number of scalars are neutral/charged under $\mathrm{SL}(2,\mathbb{Z})$, and use this feature to deduce their non-perturbative completion. The mixed NSNS/RR structures that cannot be deduced from the pure NSNS sector allow us to unambiguously fix the kinematics, which turns out to be the same for tree level and one loop. In Type IIA, these structures are essential for establishing agreement of string-theoretic corrections with the circle reduction of M-theory higher-derivative couplings.

In Jackiw-Teitelboim (JT) gravity, which is dual to a random matrix ensemble, the annealed entropy differs from the quenched entropy at low temperatures and goes negative. However, computing the quenched entropy in JT gravity requires a replica limit that is poorly understood. To circumvent this, we define an intermediate quantity called the semi-quenched entropy, which has the positivity properties of the quenched entropy, while requiring a much simpler replica trick. We compute this in JT gravity in different regimes using i) a bulk calculation involving wormholes corresponding to the Airy limit of the dual matrix integral and ii) a boundary calculation involving one-eigenvalue instanton saddles proposed by Hernández-Cuenca, demonstrating consistency between these two calculations in their common regime of validity. We also clarify why similar one-eigenvalue instanton saddles cannot be used to compute the quenched entropy due to a breakdown of the saddle-point approximation for the one-eigenvalue instanton in the replica limit.

We study the scattering and absorption properties of charged scalar fields on a near-extremal Reissner-Nordström black hole background. We show that in this low-temperature regime the near-horizon throat experiences large quantum fluctuations, whose leading contribution is described by the one dimensional Schwarzian effective action, while the soft $U(1)$ gauge modes can only contribute to subleading order. We investigate the role of the leading quantum effects both inside and outside the superradiant regime. These effects result in an enhanced reflection coefficient within the superradiant regime, while causing a suppression in the non-superradiant regime. On the other hand, the absorption cross-section increases in both regimes. Additional physical features appear as kinks in the reflection coefficient and absorption cross-section plots, corresponding to the shutdown of absorption in the superradiant regime and of stimulated emission in the non-superradiant regime.

Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant-time slice in a flat spacetime. Our prescriptions starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes in general a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and show that it leads to results with self-consistent physical properties of temporal entanglement.

Exotic entanglement entropy scaling properties usually come with interesting entanglement structures in real space and novel metrics of the spacetime lattice. One prominent example is the rainbow chain where lattice sites symmetric about the center form entangled Bell pairs due to an effective long-range coupling from the strong inhomogeneity of the coupling strength. This manuscript generalizes the rainbow chain to higher dimensional space on lattices with Hausdorff dimension one and enlarged local Hilbert space keeping the Hamiltonian frustration free. The effective Hamiltonian from the Schrieffer-Wolf transformation is given by a stacking of layers of $k$-simplices with $0$-dimensional (fully-connected) antiferromagnetic Hamiltonians, which can be diagonalized analytically with Young operators. The original lattice can be obtained from proliferating disinclination defects in a regular $k$-dimensional cubical lattice, which introduces curvature at the center of the lattice. The model interpolates between the SYK model and the free-fermionic XX spin chain, and hence might be potentially useful in understanding black hole physics and holography.

Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept of virtual quantum Markov chains (VQMCs), focusing on scenarios where subsystems retain classical information about global systems from measurement statistics. As a generalization of quantum Markov chains, VQMCs characterize states where arbitrary global shadow information can be recovered from subsystems through local quantum operations and measurements. We present an algebraic characterization for virtual quantum Markov chains and show that the virtual quantum recovery is fully determined by the block matrices of a quantum state on its subsystems. Notably, we find a distinction between two classes of tripartite entanglement by showing that the W state is a VQMC while the GHZ state is not. Furthermore, we introduce the virtual non-Markovianity to quantify the non-Markovianity of a given quantum state, which also assesses the optimal sampling overhead for virtually recovering this state. Our findings elucidate distinctions between quantum Markov chains and virtual quantum Markov chains, extending our understanding of quantum recovery to scenarios prioritizing classical information from measurement statistics.

The effective action for quantum gravity coupled to matter contains corrections arising from the functional measure. We analyse the effect of such corrections for anisotropic self-gravitating compact objects described by means of the gravitational decoupling method applied to isotropic solutions of the Einstein field equations. In particular, we consider the Tolman IV solution of general relativity and show that quantum gravity effects can modify the effective energy density as well as the effective tangential and radial pressures. For a suitable choice of the mimicking constant, upper bounds on the quantum corrections can be driven by the surface redshift of the anisotropic compact stellar system obtained with the gravitational decoupling.

We demonstrate that a $\sim 2 \sigma$ discrepancy with the Planck-$\Lambda$CDM cosmology in DESI Luminous Red Galaxy (LRG) data in the redshift range $0.4 < z < 0.6$ with effective redshift $z_{\textrm{eff}} = 0.51$ translates into an unexpectedly large $\Omega_m$ value, $\Omega_m = 0.67^{+0.18}_{-0.17}$. We independently confirm that this anomaly drives the preference for $w_0 > -1$ in DESI data \textit{alone} confronted to the $w_0 w_a$CDM model. Given that LRG data at $z_{\textrm{eff}} = 0.51$ is at odds with Type Ia supernovae in overlapping redshifts, we expect that this anomaly will decrease in statistical significance with future DESI data releases leaving an increasing $\Omega_m$ trend with effective redshift at higher redshifts. We estimate the current significance of the latter in DESI data at $\sim 1.8 \sigma$ and comment on how it dovetails with independent observations. It is imperative to understand what makes DESI LRG data at $z_{\textrm{eff}} = 0.51$ an outlier when it comes to $\Omega_m$ determinations.

Infrared singularities in perturbative Quantum Chromodynamics (QCD) are captured by the Soft function, which can be calculated efficiently using Feynman diagrams known as webs. The starting point for calculating Soft function using webs is to compute the web mixing matrices using a well known replica trick algorithm. We present a package implemented in Mathematica to calculate these mixing matrices. Along with the package, we provide several state-of-the art computations.

While the early literature on black holes focused on event horizons, subsequently it was realized that their teleological nature makes them unsuitable for many physical applications both in classical and quantum gravity. Therefore, over the past two decades, event horizons have been steadily replaced by quasi-local horizons which do not suffer from teleology. In numerical simulations event horizons can be located as an `after thought' only after the entire space-time has been constructed. By contrast, quasi-local horizons naturally emerge in the course of these simulations, providing powerful gauge-invariant tools to extract physics from the numerical outputs. They also lead to interesting results in mathematical GR, providing unforeseen insights. For example, for event horizons we only have a qualitative result that their area cannot decrease, while for quasi-local horizons the increase in the area during a dynamical phase is quantitatively related to local physical processes at the horizon. In binary black hole mergers, there are interesting correlations between observables associated with quasi-local horizons and those defined at future null infinity. Finally, the quantum Hawking process is naturally described as formation and evaporation of a quasi-local horizon. This review focuses on the dynamical aspects of quasi-local horizons in classical general relativity, emphasizing recent results and ongoing research.

These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by the topology of spaces that are used as modules to build the quantum mechanical model, while expectation values and probabilities are given by topological invariants of spaces, knots and links. The notes focus on the specific way the topology encodes quantum mechanical features, or, equivalently, on how these features can be controlled through the topology. A topological classification of entanglement is discussed, as well as properties of entanglement entropy and basic quantum protocols. The primary aim is to build a less conventional diagrammatic intuition about quantum mechanics, expanding the paradigm of ``Quantum Picturalism".

The recent observational evidence of deviations from the $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model points towards the presence of evolving dark energy. The simplest possibility consists of a cosmological scalar field $\varphi$, dubbed quintessence, driving the accelerated expansion. We assess the evidence for the existence of such a scalar field. We find that, if the accelerated expansion is driven by quintessence, the data favour a potential energy $V(\varphi)$ that is concave, i.e., $m^2=d^2V/d\varphi^2<0$. Furthermore, and more significantly, the data strongly favour a scalar field that is non-minimally coupled to gravity (Bayes factor $\log(B) = 7.34 \pm 0.6$), leading to time variations in the gravitational constant on cosmological scales, and the existence of fifth forces on smaller scales. The fact that we do not observe such fifth forces implies that either new physics must come into play on non-cosmological scales or that quintessence is an unlikely explanation for the observed cosmic acceleration.

In this work, we develop a generic formalism for the study of tensor perturbations induced at second order by first-order vector metric perturbations, dubbing these induced tensor modes $\textit{vector-induced gravitational waves}$ (VIGWs). Notably, considering an inflation-inspired power-law type magnetic field power spectrum of the form $P_B(k)\propto k^{n_\mathrm{B}}$ (where $n_{\rm B}$ is the magnetic spectral index), we show that the VIGW signal is enhanced for stiff post-inflationary EoS, with the maximum enhancement happening for $w=1$. We explicitly demonstrate this contribution is dominant over the first-order magnetically-sourced GWs. The VIGW spectrum exhibits a maximum at around the scale crossing the cosmological horizon at the end of reheating, $k_\mathrm{reh}$, with its present day peak amplitude scaling as $\Omega_{\rm GW}(k_{\rm reh},\eta_0)\propto \Delta N_{\rm reh}\times(H_{\rm inf}/M_{\rm Pl})^{8}$, where $H_{\rm inf}$ is the Hubble parameter at the end of inflation and $\Delta N_{\rm reh}$ the duration of the post-inflationary era in $e$-folds. For $w=1$ (kination) and $n_{\rm B}>-3/2$, one further obtains a nearly $n_{\rm B}$-independent frequency scaling of the GW spectrum of the form $\Omega_{\rm GW}(f,\eta_0)\propto \left(\frac{f}{f_{\rm reh}}\right)^{-2.8}$ for $f>f_\mathrm{reh}\equiv k_\mathrm{reh}/(2\pi)$. Finally, we highlight that the VIGW signal can be well within the detection bands of several next-generation interferometric GW missions at small scales. Indicatively, for $H_{\rm inf} \sim O(10^{7})\:\mathrm{GeV}$ and $O(10^{14})\:\mathrm{GeV}$, and $\Delta N_{\rm reh} \sim 15$ and $10$, the VIGW signal is expected to be detectable by LISA and ET respectively.

Energy-energy correlator (EEC) is an event shape observable that characterizes the distribution of energy flux in collision events. We initiate the study of full-range EEC at hadron colliders, generalizing the extensively studied EEC in $e^+e^-$ collision as well as the transverse EEC in hadron collisions. We derive celestial blocks from Lorentz symmetry to perform partial wave decomposition of the EEC at hadron colliders. These celestial blocks are essentially conformal blocks on the 2d celestial sphere, which have additional dependence on the collinear spin of ``light-ray transition matrix'' along the collision axis. In this work, we perform the first leading-order (LO) analytic calculation of this observable in pure Yang-Mills theory and use it as an example to illustrate the block decomposition. Numerically, the block expansion demonstrates superior accuracy in the collinear limit compared to conventional power series expansion. Analytically, we observe in this example that the block coefficients exhibit analyticity in both collinear and transverse spin. In addition, we analyze several kinematic limits at LO -- collinear, back-to-back, opposite coplanar and Regge limit. While the first three limits naturally generalize their $e^+e^-$ collision counterparts or transverse EEC and are governed by soft-collinear dynamics, the Regge limit requires complete angular dependence and reveals BFKL physics. Phenomenologically, we propose a realistic experimental setup and briefly discuss how the convolution of parton distribution function modifies the perturbative EEC result. Our work suggests that the full-range EEC at hadron colliders is an elegant observable which probes a broader kinematic space and connects various regimes of different QCD dynamics through a single measurement.

We present a comprehensive study of the two-flavor Quark--Meson--Diquark (QMD) model by comparing a renormalization approach with a renormalization-group (RG) consistent mean-field formulation based on the functional renormalization group (FRG). The renormalized QMD model allows analytical investigations of key quantities such as the zero-temperature diquark gap and the critical temperature for color superconductivity, ultimately reproducing the exact BCS relation in the high-density limit. We carry out the same analysis for different schemes of RG-consistent QMD models. We show that the RG-consistent approach yields a phase diagram and thermodynamic properties qualitatively similar to those of the renormalized model, provided both are embedded within a unified scheme that ensures consistent vacuum properties. In particular, both treatments recover the Stefan--Boltzmann limit at high densities. On the other hand, whether the BCS relation for the critical temperature is satisfied depends on the details of the RG-consistent setup. Our results highlight the relevance of renormalization and RG-consistent methods for accurately capturing the thermodynamics of QMD and related effective models with diquark degrees of freedom.

The generalized thermodynamic extremum relation, as proposed by Goon and Penco, establishes a novel theoretical framework for the study of spacetime thermodynamics. However, extant investigations generally assume that the black hole state parameter is solely a first-order function of the perturbation parameter when exploring the Goon-Penco relation in diverse spacetime contexts. An analytic expression for the perturbation parameter as a function of the black hole entropy can be expressed by treating the black hole mass as constant. The present study addresses this limitation and provides insight into the universal Goon-Penco relation when multiple thermodynamic state parameters behave as higher order functions of the perturbation parameters. Notably, we have not only established a universal relational formula in the case of multiple state variables, but more importantly, we have put forward an innovative conjecture that reveals the existence of a universal relation between displaced thermodynamic quantities in spacetime in the context of an arbitrary black hole. These theoretical breakthroughs are expected to open up new exploration directions for quantum gravity research.

We investigate the collective dynamics of multivortex assemblies in a two dimensional (2D) toroidal fluid film of distinct curvature and topology. The incompressible and inviscid nature of the fluid allows a Hamiltonian description of the vortices, along with a self-force of geometric origin, arising from the standard Kirchhoff-Routh regularization procedure. The Hamiltonian dynamics is constructed in terms of $q$-digamma functions $\Psi_q(z)$, closely related to the Schottky-Klein prime function known to arise in multiply connected domains. We show the fundamental motion of the two-vortex system and identify five classes of geodesics on the torus for the special case of a vortex dipole, along with subtle distinctions from vortices in quantum superfluids. In multivortex assemblies, we observe that a randomly initialized cluster of vortices of the same sign and strength (chiral cluster) remains geometrically confined on the torus, while undergoing an overall drift along the toroidal direction, exhibiting collective dynamics. A cluster of fast and slow vortices also show the collective toroidal drift, with the fast ones predominantly occupying the core region and the slow ones expelled to the periphery of the revolving cluster. Vortex clusters of mixed sign but zero net circulation (achiral cluster) show unconfined dynamics and scatter all over the surface of the torus. A chiral cluster with an impurity in the form of a single vortex of opposite sign also show similar behavior as a pure chiral cluster, with occasional ``jets" of dipoles leaving and re-entering the revolving cluster. The work serves as a step towards analysis of vortex clusters in models that incorporate harmonic velocities in the Hodge decomposition.

We extend the Symmetry Topological Field Theory (SymTFT) framework beyond internal symmetries by including geometric data that encode spacetime symmetries. Concretely, we enrich the SymTFT of an internal symmetry by spacetime symmetries and study the resulting symmetry-enriched topological (SET) order, which captures the interplay between the spacetime and internal symmetries. We illustrate the framework by focusing on symmetries in 1+1D. To this end, we first analyze how gapped boundaries of 2+1D SETs affect the enriching symmetry, and apply this within the SymTFT framework to gauging and detecting anomalies of the 1+1D symmetry, as well as to classifying 1+1D symmetry-enriched phases. We then consider quantum spin chains and explicitly construct the SymTFTs for three prototypical spacetime symmetries: lattice translations, spatial reflections, and time reversal. For lattice translations, the interplay with internal symmetries is encoded in the SymTFT by translations permuting anyons, which causes the continuum description of the SymTFT to be a foliated field theory. Using this, we elucidate the relation between Lieb-Schultz-Mattis (LSM) anomalies and modulated symmetries and classify modulated symmetry-protected topological (SPT) phases. For reflection and time-reversal symmetries, the interplay can additionally be encoded by symmetry fractionalization data in the SymTFT, and we identify mixed anomalies and study gauging for such examples.

In this note the Hamiltonian formulation of four-dimensional gravity, in the Palatini-Cartan formalism, is recovered by elimination of an auxiliary field appearing as part of the connection.

We report some new findings regarding the subtle relations among geodesic completeness, curvature singularities and tidal forces. It is well known that any particle may be torn up near a singularity at the center of a black hole due to the divergent tidal force. However, we find that singularity is not the only cause of tidal force divergence. Even on the surface of the Earth, the tidal force experienced by a particle could be arbitrarily large if the particle moves arbitrarily close to the speed of light in a nonradial direction. Usually, a curvature singularity implies geodesic incompleteness since in many cases the metric cannot be defined at the location of the singularity. Counterexamples have been found in recent years, suggesting that geodesics could pass through curvature singularities. By taking into account the fact that any real particle is an extended body, we calculate the tidal force acting on the particle in a static and spherically symmetric spacetime. We explicitly show that an infinite tidal force always occurs near such a singularity. Therefore, no particle can actually reach the curvature singularity even if the metric is well defined at that point. We also show that the tidal acceleration along a null geodesic at the coordinate origin is divergent. For a wormhole solution that has a curvature singularity at the throat but possesses a regular metric, we show that the tidal force on any particle passing through the throat is divergent.

The Standard Model of particle physics is derived from first principles starting from the free Dirac Lagrangian. All known fermionic particle species plus three right handed neutrinos are obtained from ideals of a $C\ell_{8,0}$ algebra, with gauge symmetries arising as rotations of creation-annihilation operators and vacua. Triality originates both the strong force and three particle families with a mass hierarchy. Lorentz and gauge transformations are unified while avoiding the Coleman-Mandula theorem. Chirality stems unavoidably from rotations leaving the vacua invariant, with a predicted Weinberg angle of $\sin^2(\theta_W)=3/8$. The theory is anomaly-free and devoid of proton decay.

We build up a complete description of QCD phase structure by applying the parametrization of the chiral and deconfinement order parameters upon the calculations from functional QCD approaches. In particular in the first order phase transition region at high chemical potential, both the phase transition line using Maxwell construction and the coexistence boundary lines from the spinodal decompostion are determined. We compute the thermodynamic quantities including the number density, the energy density, the pressure and also the free energy for both stable and unstable phases of QCD. Additionally, after applying a phenomenological description of the inhomogeneity of the QCD free energy, we obtain the surface tension of the first order phase transition of QCD.