Entanglement islands have played a key role in the recent derivation of the Page curve and other progress on the black hole information problem. Arising from the inclusion of connected wormhole saddles in a gravitational replica trick, islands signal that degrees of freedom in the black hole interior are not microscopically independent of the exterior Hawking radiation. Islands were originally discovered in the context of AdS/CFT coupled to an external, nongravitating reservoir, where the coupling gives graviton excitations an anomalous boundary scaling dimension (or "mass"). It has been claimed in the literature that this mass is crucial for the existence of islands and even the Page curve itself. In this paper, however, we explain how entanglement islands can also appear in setups with massless gravitons and no external reservoir, giving a number of examples including the entanglement wedges of boundary CFT regions, of radiation at null infinity in asymptotically flat spacetimes, and of radiation inside a semiclassical but gravitating spacetime. In each case, the Page curve is physically observable and can be determined with sufficiently careful experiments on many copies of the black hole. We give general arguments for the existence of gauge-invariant operators in gravity which are compactly supported to all orders in perturbation theory (whenever no isometries of the background spacetime exist) and refine a recently-proposed explicit construction of such operators. When applied to islands, these results -- together with entanglement wedge reconstruction -- guarantee that semiclassical operators in the island can be approximated by nonperturbative operators on the Hawking radiation.

We derive a universal bound on the integrated total scattering cross-section at \emph{finite} energies, expressed in terms of a single low-energy coefficient constrained by the non-perturbative S-matrix Bootstrap. At high energies, the bound is compared with proton-proton scattering data; at low energies, with numerical bootstrap results obtained by directly maximizing the cross-section. We conjecture that the amplitude saturating the cross-section at high energies lies at a strongly-coupled corner of the allowed space of low-energy parameters. This universal amplitude exhibits a rising total cross-section, a shrinking elastic differential cross-section with multiple diffractive minima, and a surprisingly rich spectrum of resonances aligning along Regge trajectories, including Pomeron-like and daughter trajectories, as well as unusual ``singular" trajectories in the forward limit which appear deeply interconnected with Froissart growth. Remarkably, the eikonal representation reveals that the scattering is localized within an annular region that slowly expands with energy, challenging the traditional ``disk" diffraction picture. Our results open the door to theoretical and phenomenological studies of \emph{soft} high-energy hadronic scattering via the S-matrix Bootstrap.

We propose a new UV-complete dark energy model which is \underbar{\it neither} a cosmological constant nor a slowly rolling scalar field. Our dark energy is the flux of a top form in a hidden sector gauge theory similar to QCD. The top form controls the vacuum energy generated by dark sector CP violation. Its flux discharges by the nucleation of membranes that source it. The tension and charge of the membranes are set by the chiral symmetry breaking scale $\sim 10^{-3} eV$, and the dark energy is a transient. It decays on the order of the current age of the universe. The decays decrease dark energy discretely and randomly, instead of gradually like rolling scalars. Since the decay rate is close to the present Hubble scale, $\Gamma \ga H_0^4$, in a time $\sim {\cal O}(1/H_0)$ the cosmic acceleration may even cease altogether.

We discuss a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. We use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space.

Domain wall fermions use a $2n$-dimensional spacetime defect embedded in $(2n+1)$-dimensional spacetime to realize massless lattice Dirac fermions. Recent work has extended this idea to realize a single unpaired Weyl fermion in a finite lattice. Here, we realize the same using a $2n$-dimensional string defect embedded in $(2n+2)$-dimensional spacetime on a finite lattice for $n=1$. This string is a lattice version of the continuum axion string described in Callan-Harvey. Our results are obtained in a Hamiltonian formulation in Minkowski spacetime. Extending the results to Euclidean spacetime and to $n>1$ is straightforward. This work has applications to lattice chiral gauge theories and axion cosmology.

We study the structure of topological defects for finite Abelian symmetries in quantum field theories, and argue on physical grounds that they satisfy the definition of a higher fusion category proposed by Johnson-Freyd. Our primary focus is on the requirement of Karoubi completeness, i.e. the factorization conditions on higher condensation defects. We demonstrate this on a tree of such defects, constructed by successive higher gauging, explicitly using Lagrangian techniques in a concrete four-dimensional example, before turning to more general field theories. Along the way we also comment on the phenomenon where decoupled topological field theories appear as fusion coefficients. We further discuss the categorical role of anomalies, and how they may affect the properties of (higher) condensation defects.

We calculate the glueball-fermion hard-scattering amplitude from the dilaton-dilatino closed string scattering amplitude in type IIB superstring theory, in the framework of the gauge/string theory duality. We investigate its high-energy scaling at fixed angle and also in the Regge limit. We derive the leading and sub-leading terms contributing to the scattering cross section. This dual calculation of the glueball-fermion scattering amplitude is particularly interesting since it involves the scattering of two different types of external states. We calculate explicitly some angular integrals for two scalar spherical harmonics and two spinor spherical harmonics on the five-sphere, leading to selection rules.

Utilizing the framework of free probability, we analyze the spectral and operator statistics of the Rosenzweig-Porter random matrix ensembles, which exhibit a rich phase structure encompassing ergodic, fractal, and localized regimes. Leveraging subordination formulae, we develop a perturbative scheme that yields semi-analytic expressions for the density of states up to second order in system size, in good agreement with numerical results. We compute higher-point correlation functions in the ergodic regime using both numerical and suitable analytic approximations. Our analysis of operator statistics for various spin operators across these regimes reveals close agreement with free probability predictions in the ergodic phase, in contrast to persistent deviations observed in the fractal and localized phases, even at late times. Notably, the fractal phase exhibits partial features of asymptotic freeness while retaining memory of the initial spectrum, highlighting the importance of non-localized eigenstates for the emergence of free probability behavior. Employing distance measures and statistical tools such as the $\chi^2$ statistic, Kullback-Leibler divergence, and Kolmogorov-Smirnov hypothesis testing, we define a characteristic time scale-the free time-that marks the onset of the validity of free probability predictions for operator spectral statistics in the ergodic phase. Remarkably, our findings demonstrate consistency across these different approaches.

We have re-analyzed the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker-Planck equation. We demonstrate that the Fokker-Planck equation reduces to a simplified form equivalent to a scaled quantum mechanical problem with a harmonic oscillator potential. In this framework, we highlight an interesting correspondence between supersymmetric quantum mechanics (SUSY QM) and the Fokker-Planck dynamics associated with the Schwarzschild metric. Utilizing the isospectral deformation, an intrinsic feature of SUSY QM, we derive a family of one-parameter isospectral potentials. Notably, this new class of potentials exhibits the same energy spectrum as the original harmonic oscillator potential, but with distinct wavefunctions.

In this study, we investigate the effect of the Lorentz invariant violation on the Casimir energy and pressure of the massive fermion field in the presence of the compact dimensions with topological $R^4\times S^1$, referring to the Kaluza-Klein model. In the system, the Dirac field is confined between two parallel plates with the geometry described by MIT bag boundary conditions, and the compactified dimension satisfies quasi-periodic boundary conditions. We investigate two directions of the Lorentz violation, namely, space- and time-like. The results reveal that in the space-like vector case, the Lorentz violation's strength and the extra dimension affect the Casimir energy and pressure. In contrast, in the time-like vector case, they are only affected by the extra dimension. We also propose an indirect method to estimate the size of the extra dimension by comparing the frequency shift of the massless fermionic case to that of the scaled experimental data for the electromagnetic field.

We consider a three-dimensional gravity model that includes (non-linear) Maxwell and Chern-Simons-like terms, allowing for the existence of electrically charged rotating black hole solutions with a static electromagnetic potential. We verify that a Cardy-like formula, based not on central charges but on the mass of the uncharged and non-spinning soliton, obtained via a double Wick rotation of the neutral static black hole solution, accurately reproduces the Bekenstein-Hawking entropy. Furthermore, we show that a slight generalization of this model, incorporating a dilatonic field and extra gauge fields, admits charged and rotating black hole solutions with asymptotic Lifshitz behavior. The entropy of these solutions can likewise be derived using the Cardy-like formula, with the Lifshitz-type soliton serving as the ground state. Based on these results, we propose a generalized Cardy-like formula that successfully reproduces the semiclassical entropy in all the studied cases.

By considering properties of the energy-momentum tensor of the electroweak magnetic monopole and its Born-Infeld extension, we attempt to make comments on the stability of these configurations. Specifically, we perform a study of the behaviour of the so-called internal force and pressure of these extended field-theoretic solitonic objects, which are derived from the energy-momentum tensor. Our method is slightly different from the so-called Laue's criterion for stability of nuclear matter, a local form of which had been proposed and applied in the earlier literature to the `t Hooft-Polyakov (HP) magnetic monopole, and found to be violated.By applying our method first to HP monopole, we also observe that, despite its topological stability, the total (finite) internal force (which has only radial components) is directed inwards, towards the centre of the monopole, which would imply instability. Thus this mechanical criterion for stability is arguably violated in the case of the HP monopole, as is the local version of Laue's criterion. The criterion is satisfied for the short-range part of the energy momentum tensor, in which the long-range part, due to the massless photon of the U(1) subgroup, is subtracted. Par contrast, the total internal force of the Cho-Maison (CM) electroweak monopole has both radial and angular components, which diverge at the origin, leading to rotational instabilities. Finally, by studying finite-energy extensions of the CM, either with non-minimal Higgs couplings with the hypercharge sector or hypercharge Born-Infeld type models, we find that the total force, integrated over space, is finite, but it has also angular components in the Born-Infeld case. The latter feature is interpreted as indicating that the Born-Infeld-CM monopole might be subject to rotations upon the action of perturbations, but it does not necessarily imply instabilities of the configuration.

We compute the leading quantum corrections to the energies of solitons which are constructed from BPS equations for two scalar fields in one space dimension. A particular feature of the considered models is that there are several translationally invariant ground states. We call them primary and secondary vacua. The former are those that are asymptotically assumed by the topologically stable solitons. Therefore the primary vacua fully determine the classical energy and solitons that occupy a secondary vacuum in finite but eventually large portions of space are classically degenerate. Then the quantum corrections to the energy are decisive for the energetically favored soliton. We find that the leading quantum correction to the energy is not bounded from below and that this correction is the more negative the larger the region is in which the soliton approaches a secondary vacuum.

We provide a new method to calculate the full microlocal description of singularities of Feynman integrals. This is done by associating a unique constructible function to the system of partial differential equations (PDEs) annihilating the integral and from this function the singularities can directly be read-off. This function can be constructed explicitly even if the system of PDEs is unknown and describes both the location of the singularities and the number of master integrals on them. Our framework is flexible enough to preform the calculation in any of the Lee-Pomeransky, Feynman, or momentum representations.

We consider the chiral anomaly for systems with a wide class of Hermitian Dirac operators ${Q}$ in 4D Euclidean spacetime. We suppose that $ Q$ is not necessarily linear in derivatives and also that it contains a coordinate inhomogeneity unrelated to that of the external gauge field. We use the covariant Wigner-Weyl calculus (in which the Wigner transformed two point Greens function belongs to the two-index tensor representation of the gauge group) and point splitting regularization to calculate the global expression for the anomaly. The Atiyah-Singer theorem can be applied to relate the anomaly to the topological index of $ Q$. We show that the topological index factorizes (under certain assumptions) into the topological invariant $\frac{1}{8\pi^2}\int \text{tr}(F\wedge F)$ (composed of the gauge field strength) multiplied by a topological invariant $N_3$ in phase space. The latter is responsible for the topological stability of Fermi points/Fermi surfaces and is related to the conductivity of the chiral separation effect.

We investigate on the diffeomorphism invariance of the effective gravitational action, focusing in particular on the path integral measure. In the literature, two different measures are mainly considered, the Fradkin-Vilkovisky and the Fujikawa one. With the help of detailed calculations, we show that, despite claims to the contrary, the Fradkin-Vilkovisky measure is diffeomorphism invariant, while the Fujikawa measure is not. In particular, we see that, contrary to naive expectations, the presence of $g^{00}$ factors in the Fradkin-Vilkovisky measure is necessary to ensure the invariance of the effective gravitational action. We also comment on results recently appeared in the literature, and show that formal calculations can easily miss delicate points.

We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not necessarily a tensor product of vector spaces over the complex numbers. The Hamiltonian is a sum of commuting projections. We also give a topological field theory construction of Levin-Wen models.

In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic combination of the anomalous dimensions remains finite at the right-most singularities, providing an efficient tool for resummation. In this paper, we analyze the small-spin behavior of the anomalous dimensions for all types of twist-two operators in the $O(N)$-symmetric $\varphi^4$ model at the four-loop level, in the complex $\varphi^3$ model at the three-loop level, and the Gross-Neveu-Yukawa model at the two-loop level. We find that the behavior of the anomalous dimensions at singular points is consistent with theoretical expectations, and we present expressions for the resummed anomalous dimensions.

We investigate the dynamics of four-dimensional $\mathcal{N}=2$ $SU(2)$ super Yang--Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function $F_{\text{AdS}}=-\log Z_{\text{AdS}}$. At weak coupling $\Lambda L \ll 1$ the maximization singles out the Dirichlet boundary condition with an $SU(2)$ boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for $\Lambda L \sim \mathcal{O}(1)$ new boundary conditions are favored, with gauge-group higgsed down to $U(1)$, matching the expectation from the flat space limit. We use supersymmetric localization to compute $Z_{\text{AdS}}$ nonperturbatively. We further provide evidence for a relation between $F_{\text{AdS}}$ and the $\mathcal{N}=2$ prepotential in AdS background.

Six dimensional $\mathcal{N}=(1,0)$ supergravity features BPS strings whose properties encode highly nontrivial information about the parent 6d theory. We focus on a distinguished set of theories whose string charge lattice is one-dimensional. In geometric theories, the generator of the lattice arises from a D3 brane wrapping the hyperplane class in $\mathbb{P}^2$. This hyperplane string is expected to remain stable even when one ventures beyond the geometric regime where it becomes challenging to verify which candidate 6d theories belong to the swampland. We identify five 6d models which from the perspective of the hyperplane string deviate the most from being geometric. For these theories we are able to provide an exact description of the left-moving sector of the hyperplane string worldsheet in terms of a rational conformal field theory and provide evidence for their consistency. In one instance, using RCFT methods we are able to determine the elliptic genus and find that in the unflavored limit it matches with the elliptic genus of geometric models. We argue that the non-geometric model is connected to geometric ones via a sequence of Higgsing transitions. These results lead us to formulate a proposal relating the quantum corrected moduli space of the hyperplane string CFT with a region of the landscape of 6d $(1,0)$ quantum gravity.

This paper demonstrates how the Veneziano partial amplitude of bosonic string theory admits a generalization to world-(hyper)surfaces of any dimension $d$. In particular, for $d=2$, by carving up the worldsheet integral according to stipulations imposed on conformal cross ratios, the Virasoro-Shapiro full amplitude can be decomposed into a sum of three partial amplitudes. The amplitudes obtained on generalizing the Veneziano amplitude all contain tachyons. To explore candidate tachyon-free and supersymmetric versions of these amplitudes, a new bootstrap principle is introduced and applied, which demands that towers of residues alternate between all-even and all-odd spin partial waves.

We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex superalgebras, there are the unitary Virasoro vertex algebras (N=0) and the unitary N=1,2,3,4 super-Virasoro vertex superalgebras. Accordingly, we have a uniform construction that gives, besides the already known N=0,1,2 super-Virasoro nets, also the new N=3,4 super-Virasoro nets. All strongly rational unitary minimal W-algebras give rise to previously known completely rational graded-local conformal nets and we conjecture that the converse is also true. We prove this conjecture for all unitary W-algebras corresponding to the N=0,1,2,3,4 super-Virasoro vertex superalgebras.

Though an anti-de Sitter (AdS) vacuum, corresponding to a negative cosmological constant (NCC), can be not responsible for the acceleration of current universe, it might coexist with one evolving positive dark energy component at low redshift, as well as with early dark energy around the recombination to solve the Hubble tension. In this paper, we investigate the scenario with one AdS vacuum around the recombination and one at low redshift, and from both current observational and theoretical perspectives preliminarily explore the possibility that the universe experienced a landscape with multiple AdS vacua since matter-radiation equality.

We revisit the computation of quasinormal modes (QNMs) of the Kerr black hole using a numerical approach exploiting a representation of the Teukolsky equation as a $2D$ elliptic partial differential equation. By combining the hyperboloidal framework with a $m$-mode decomposition, we recast the QNM problem into a genuine eigenvalue problem for each azimuthal mode. This formulation enables the simultaneous extraction of multiple QNMs, traditionally labelled by overtone number $n$ and angular index $\ell$, without requiring prior assumptions about their structure. We advocate for a simplified notation in which each overtone is uniquely labelled by a single index $q$, thereby avoiding the conventional but artificial distinction between regular and mirror modes. We compare two distinct hyperboloidal gauges-radial fixing and Cauchy horizon fixing-and demonstrate that, despite their different geometric properties and behaviour in the extremal limit, they yield numerical values for the QNM spectra with comparable accuracy and exponential convergence. Moreover, we show that strong gradients observed near the horizon in the extremal Kerr regime are coordinate artefacts of specific slicing rather than physical features. Finally, we investigate the angular structure of the QNM eigenfunctions and show that the $m$-mode approach allows flexible projection onto both spin-weighted spheroidal and spherical harmonic bases. These results underscore the robustness and versatility of the hyperboloidal $m$-mode method as a foundation for future studies of QNM stability, pseudospectra, and mode excitation in gravitational wave astronomy.

Dark matter may freeze-out and undergo composite assembly while decoupled from the Standard Model. In this secluded composite scenario, while individual dark matter particles may be too weakly-coupled to detect, the assembled composite can potentially be detected since its effective coupling scales with number of constituents. We examine models and observables for secluded composites, and in particular we investigate the cosmological abundance of the composite binding field, which is generated during freeze-out annihilation and secluded composite assembly. This binding field could be discovered as a new relativistic species in the early universe or through later interactions as a subdominant dark component.

We discuss a modification of a recently developed numerical scheme for evolving spherically symmetric self-gravitating systems to include the effects of self-interacting dark matter. The approach is far more efficient than traditional N-body simulations and cross sections with different dependencies on velocity and scattering-angle are easily accommodated. To demonstrate, we provide results of a simulation, which runs quickly on a personal computer, that shows the expected initial flattening of the inner region of an NFW halo as well as the later gravothermal collapse instability that leads to a dense core at the galactic center. We note that this approach can also be used, with some augmentation, to simulate the dynamics in globular clusters by modeling gravitational hard scattering as a self-interaction.

We show that the Luttinger-Ward functional can be formulated as an operator insertion in the path integral and hence can be thought of as a generalized symmetry. The key result is that the associated charge, always quantized, defines the homotopy, not the physical charge. The disconnect between the two arises from divergences in the functional or equivalently zeros of the single-particle Green function. Such divergences produce an anomaly of the triangle-diagram type. As a result of this anomaly, we are able to account for the various deviations\cite{rosch,dave,altshuler,osborne,l3,l5} of the Luttinger count from the particle density. As a consequence, non-Fermi liquids can be classified generally by the well known anomaly structures in particle physics. Charges descending from generalized symmetries, as in the divergence of the Luttinger-Ward functional, are inherently non-local, their key experimental signature.

We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a L\'evy Stable (fat-tailed) distribution. L\'evy random matrices are known to demonstrate non-ergodic behaviour through the emergence of a mobility edge. We study the eigenvalue distribution, focusing on long- and short-range correlations and extreme statistics. This model demonstrates a crossover from chaotic to integrable behaviour (in the spectral correlations) as the distribution becomes increasingly fat-tailed. We investigate this crossover through a hierarchical analysis of the eigenvalue spectrum, based on the multi-fractal hierarchy of the L\'evy Stable distribution. The crossover is explained in terms of a genuine many-body effect, distinct from the transition (controlled by a mobility edge) in the L\'evy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.

Trace-free Einstein gravity, in the absence of matter fields and using the Friedmann-Robertson-Walker (FRW) metric, is solvable both classically and quantum mechanically. This is achieved by using the conformal time as the time variable and the negative or positive of the inverse of the scale factor as configuration variable to write the classical equation of motion, which turns out to be the one of a free particle ($k=0$), a harmonic oscillator ($k=1$), and a repulsive oscillator ($k=-1$) in the real half-line. In all cases, the observable identified as the cosmological constant is six times the Hamiltonian. In particular, for a closed Universe ($k=1$), spacetime exhibits a cyclic evolution along which the scalar curvature is constant and finite, thereby avoiding singularities. The quantum theory is reached by using canonical quantization. We calculate the spectrum of the observable corresponding to the cosmological constant. Remarkably, for the closed Universe ($k=1$), the spectrum is discrete and positive while for flat ($k=0$) and open ($k=-1$) universes, the spectra are continuous. Heisenberg's uncertainty principle imposes limitations on the simultaneous measurement of the Hubble expansion (momentum variable) and the configuration variable. We also report the observable identified as the cosmological constant for inflaton, phantom and perfect fluids coupled to trace-free Einstein gravity in the FRW metric.

Axions are hypothetical particles that could address both the strong charge-parity problem in quantum chromodynamics and the enigmatic nature of dark matter. However, if axions exist, their mass remains unknown, and they are expected to interact very weakly with the electromagnetic field, which explains why they have not been detected yet. This study proposes a way to substantially augment the axion-photon interaction by confining the photons within high-quality-factor dielectric resonators, increasing their intensity and lifetime and thus the possibility of interacting with axions in the background. In view of this, we study resonant axion-mediated photonic transitions in millimeter-sized spherical dielectric resonators, based on fully analytical calculations to the first order in perturbation theory. Such resonators exhibit high lifetime Mie resonances in the microwave part of the spectrum, with a separation that can be tailored with the radius of the sphere to match the expected axion frequency, allowing axion-mediated photonic transitions when particular selection rules are fulfilled. Such transitions are expected to be enhanced by more than ten orders of magnitude in the presence of the resonator, compared to transitions occurring in homogeneous space.

We study Parity Violating Gravity Theories whose gravitational Lagrangian is a generic function of the scalar curvature and the parity odd curvature pseudoscalar, commonly known as the Holst (or Hojmann) term. Generalizing some previous results in the literature, we explicitly show that if the Hessian of this function is non-degenerate, the initial non-Riemannian Theory is on-shell equivalent to a metric Scalar-Tensor Theory. The generic form of the kinetic coupling function and the scalar potential of the resulting Theory are explicitly found and reported.

Light scalar or vector particles are among the most studied dark matter candidates. Yet, those are always described as scalar or vector fields. In this paper, we explore instead the embedding of the scalar particle in an antisymmetric rank-three tensor field, and the dark photon into an antisymmetric rank-two tensor field (a so-called Kalb-Ramond field), and construct minimal bases of effective interactions with Standard Model fields. Then, keeping phenomenological applications as our main objective, a number of theoretical aspects are clarified, in particular related to the impact of existing dualities among the corresponding free theories, and concerning their Stueckelberg representations. Besides, for the rank-two field, we present for the first time its full propagator, accounting for the possible presence of a pseudoscalar mass term. Thanks to these results, and with their different kinematics, gauge-invariant limits, and Lorentz properties, we show that these higher-form fields provide genuine alternative frameworks, with different couplings and expected signatures at low-energy or at colliders.

In this work we obtain a numerical self-consistent spherical solution of the semiclassical Einstein equations representing the evaporation of a trapped region which initially has both an outer and an inner horizon. The classical matter source used is a static electromagnetic field, allowing for an approximately Reissner-Nordstr\"om black hole as the initial configuration, where the charge sets the initial scale of the inner horizon. The semiclassical contribution is that of a quantum scalar field in the "in" vacuum state of gravitational collapse, as encoded by the renormalised stress-energy tensor in the spherical Polyakov approximation. We analyse the rate of shrinking of the trapped region, both from Hawking evaporation of the outer apparent horizon, as well as from an outward motion of the inner horizon. We also observe that a long-lived anti-trapped region forms below the inner horizon and slowly expands outward. A black-to-white-hole transition is thus obtained from purely semiclassical dynamics.

Gauge-invariant field strengths, defined as parallel transports to infinity of ordinary field strengths, naturally emerge in a few physical phenomena governed by $QCD$. One of them is confinement of colour. Despite the arbitrariness in their definition coming from the freedom in the choice of the path of the parallel transport to infinity, the request of differentiability with respect to the position $x$ strongly constrains their correlation functions. Strong constraints also come from translation and Lorentz invariance. Gauge invariant field strengths also appear in the non abelian Stokes theorem, and allow to understand basic properties of the vacuum by use of lattice data.

We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The cellular automata considered are examples of linearly degenerate systems where two distinct mechanisms of diffusion, namely normal and convective diffusion, coexist. Our formalism, based on macroscopic fluctuation theory, allows us to describe current fluctuations stemming from these two diffusive processes, and we expect it to be applicable to generic linearly degenerate systems. The derived probability distributions match the exact microscopic result and numerical simulations.

This paper presents a new conformal symmetry of stationary, axisymmetric Kerr perturbations. This symmetry is exact but non-geometric (or "hidden"), and each of its generators has an associated infinite family of eigenstate solutions. Tidal perturbations of a black hole form an irreducible highest-weight representation of this conformal group, while the tidal response fields live in a different such representation. This implies that black holes have no tidal deformability, or vanishing Love numbers.

Topologically ordered matter phases have been regarded as beyond the Landau-Ginzburg symmetry breaking paradigm of matter phases. Recent studies of anyon condensation in topological phases, however, may fit topological phases back in the Landau-Ginzburg paradigm. To truly do so, we realized that the string-net model of topological phases is in fact an effective lattice gauge theory coupled with anyonic matter once two modifications are made: (1) We reinterpret anyons as matter fields coupled to lattice gauge fields, thus extending the HGW model to a genuine Hamiltonian lattice gauge theory. (2) By explicitly incorporating the internal degrees of freedom of anyons, we construct an enlarged Hilbert space that supports well-defined gauge transformations and covariant coupling, restoring the analogy with conventional lattice gauge field theory. In this modified string-net model, topological phase transitions induced by anyon condensation and their consequent phenomena, such as order parameter fields, coherent states, Goldstone modes, and gapping gauge degrees of freedom, can be formulated exactly as Landau's effective theory of the Higgs mechanism. To facilitate the understanding, we also compare anyon condensation to/with the Higgs boson condensation in the electroweak theory and the Cooper pair condensation.

In this paper, we introduce a ``CFT factory'' : a novel algorithm of methodically generating 2D lattice models that would flow to 2D conformal fixed points in the infrared. These 2D models are realised by giving critical boundary conditions to 3D topological orders (symTOs/symTFTs) described by string-net models, often called the strange correlators. We engineer these critical boundary conditions by introducing a commensurate amount of non-commuting anyon condensates. The non-invertible symmetries preserved at the critical point can be controlled by studying a novel ``refined condensation tree''. Our structured method generates an infinite family of critical lattice models, including the A-series minimal models, and uncovers previously unknown critical points. Notably, we find at least three novel critical points (c$\approx 1.3$, $1.8$, and $2.5$ respectively) preserving the Haagerup symmetries, in addition to recovering previously reported ones. The condensation tree, together with a generalised Kramers-Wannier duality, predicts precisely large swathes of phase boundaries, fixes almost completely the global phase diagram, and sieves out second order phase transitions. This is not only illustrated in well-known examples (such as the 8-vertex model related to the $A_5$ category) but also further verified with precision numerics, using our improved (non-invertible) symmetry-preserving tensor-network RG, in novel examples involving the Haagerup symmetries. We show that critical couplings can be precisely encoded in the categorical data (Frobenius algebras and quantum dimensions in unitary fusion categories), thus establishing a powerful, systematic route to discovering and potentially classifying new conformal field theories.