Papers

Finite-$N$ trace relations reorganize the Hilbert space of gauge-invariant operators beyond the freely generated large-$N$ description. We study this structure using the Hironaka decomposition of the invariant ring of $d$ Hermitian $N\times N$ matrices. We first prove that the primary invariants may always be chosen to be homogeneous single-trace operators. We then show that, for any such choice, a nontrivial secondary invariant must appear by degree $L_{N,d}=2\log_d N+\log_d\log_d N+\mathcal{O}_d(1)$, which is parametrically below the first universal trace identity at degree $N+1$. This is a global overcrowding effect: exponentially many independent short single traces compete for only $1+(d-1)N^2$ algebraically independent coordinates. The overcrowding scale matches the fastest scrambling times expected for fast scramblers. We argue that this agreement of scales is not accidental: overcrowding provides a microscopic algebraic picture of scrambling in matrix models. Low-rank examples show that secondary invariants can distinguish configurations with identical primary data and, for suitable dynamics, label semiclassical sectors connected by instantons. These results identify the Hironaka decomposition as a natural framework for organizing perturbative and intrinsically finite-$N$ information in collective descriptions of gauge theories.

In general relativity and its metric-formalism extensions, the innermost stable circular orbit and the photon ring of a charged black hole contract as the charge increases. In this paper, we discover a qualitative anomaly that violates this universal behavior, serving as a smoking-gun signature of geometric nonmetricity. By considering a minimal coupling between the bosonic field and the independent affine metric, we demonstrate that nonmetricity induces an effective geometric force that triggers a trajectory expansion of both massless and massive bosons with increasing black hole charge. This qualitative inversion directly imprints onto the black hole shadow, lifting the degeneracy between metric-affine gravity and general relativity. Using Eddington-inspired Born-Infeld gravity as a concrete implementation, we show that next-generation horizon-scale imaging can resolve this signature, probing a complementary high-energy window up to the $10^{5}_{~}\,\text{TeV}$ scale.

The present work pursues the investigation of the physics of a planar electromagnetic system incorporating nonlinear effects, as well as de Broglie-Proca and Chern-Simons mass terms in vacuum, which can be tuned to describe new planar metamaterials (MTMs) potentially suitable for technological applications. As a result, we observe interesting effects generated by a spatially dispersive profile that emerges from non-linearity. This characterizes the three-dimensional QED vacuum as a nonlocal metamaterial. The constitutive relations are derived, and the dielectric function of the metamaterial (MTM) exhibits spatial dispersion due to the Chern-Simons mass. The dispersion relations are analyzed in terms of applied external electromagnetic fields and both the de Broglie-Proca and Chern-Simons mass parameters. We also notice that, in the special case in which only a background magnetic field is present, this field gives no contribution neither to the dielectric function nor to the spatial dispersion profile, as is the case when both the electric and magnetic fields are present.

We study the scalar and Dirac perturbations of quantum-corrected black holes with cosmological constant. Using two different methods (WKB and double-null characteristic integration) we compute the quasinormal modes (QNMs) of de Sitter and Anti-de Sitter solutions considering linear field perturbations in the background geometry. In the limit of general relativity black holes our methods demonstrate good convergence with the available results in literature. In the presence of an extra quantum parameter we verify that all perturbations are stable evolving in towers of quasinormal oscillations. We scrutinize the spectra of both dS and AdS solutions studying the influence of that extra parameter in the frequencies.

The Unruh effect predicts that an accelerating observer perceives the Minkowski vacuum as a thermal bath, yet direct detection remains experimentally inaccessible. Its timelike counterpart, arising from the entanglement of massless fields between the future and past light cones, offers a more feasible route but requires a detector whose transition frequency follows a specific conformal-time scaling. We propose and analyze a practical implementation of such a detector using superconducting fluxonium circuits, which naturally provide two quasi-degenerate ground states and a tunable excited state, forming an effective $\Lambda$-system. By modulating the excited-state transition frequency in Minkowski time, the detector accumulates a geometric phase associated with the timelike Unruh effect. Open-system simulations predict $\sim 10\%$ shift in the ground-state population within $530$ ns, representing a three-order-of-magnitude sensitivity enhancement over two-level Unruh-DeWitt detectors. These results establish a realistic quantum-circuit platform for experimentally probing the timelike Unruh effect and, more broadly, for testing fundamental nature of quantum fields using engineered quantum systems.

We revisit Kerr-NUT metrics and related spin-$s$ fields in $D\geq4$, and study their associated scattering amplitudes. Starting in position space, we highlight the interpretation of mass and (multiple) NUT charges as being associated to distinct solutions of the rotation-deformed radial equation, which is made explicit in Cartesian multi-Kerr-Schild coordinates. This interpretation extends to electromagnetism with magnetic-type charges, and also extends to higher-spin counterparts, in accordance with the classical double or multi copy. We then establish a notion of “electric-magnetic" duality in higher dimensions, relating mass/electric to NUT/magnetic charges, which generalises the $D=4$ case in a novel manner. For $D\geq6$, this involves the choice where the multiple magnetic charges are equal. The duality is revealed in momentum space, by the 3-point scattering amplitudes that generate the solutions. For all spins, these amplitudes are constructed from a spin-raising operator $\mathcal S_\mu$ and take the form $\varepsilon^{\mu_1\cdots\mu_s}{\mathcal S}_{\mu_1}\cdots {\mathcal S}_{\mu_s}$ acting on a scalar seed. The scalar seed of the electric sector is dual to that of the magnetic sector: where the former's rotation dependence resums to a Bessel function $J_{\frac{D-5}{2}}$, the latter resums to a Bessel function $J_{-\frac{D-5}{2}}$. Finally, we explore the notion of self-duality that arises from this picture. Studying the classical $2\!\mapsto\!2$ amplitudes that determine leading-order scattering, we find no evidence of a higher-dimensional analogue of the integrability of $D=4$ self-dual gravity.

We provide the first complete calculation of the leading contribution to the decoherence of primordial fluctuations in the scalar part of the metric fluctuations within simplest, single-clock, inflationary models, assuming decoherence comes from gravitational interactions with an environment made up of the other, unmeasured, short-wavelength scalar and tensor modes. We include the contributions from all of the contributing interactions at leading order in powers of $(H/M_p)^2$ and of the slow-roll parameter $\epsilon_1$. Unlike all extant calculations in the literature we find a result that is not slow-roll suppressed (and so is the same order of magnitude as tensor-mode decoherence). The difference arises because the dominant decoherence comes from interactions that involve both the tensor and scalar environments simultaneously (and so are missed when they are examined separately). We verify that the leading contributions to decoherence are UV finite (as they must be). We confirm that the interactions driving decoherence become time-local and Gaussian in the deep super-Hubble inflationary regime and show how this can be used to reliably compute the evolution of the purity in the late-time regime relevant for observations (where naive perturbation theory is known to break down). The same derivation shows explicitly why the effects that undermine perturbation theory for decoherence do not also undermine the basic inflationary prediction for the amplitude of primordial fluctuations (in agreement with general arguments).2

We study a modification of the model of axion inflation coupled to a $U(1)$ gauge field where the vector field is massive. In the conventional scenario with a massless gauge field, the onset of the regime where the gauge field strongly backreacts on the inflaton displays an instability whose nonlinear evolution and endpoint remain poorly understood. We argue that, if the gauge field is massive enough, the transition to the strong backreaction regime instead occurs smoothly, avoiding this instability. This observation suggests that axion inflation with massive gauge fields admits a controllable strong backreaction regime, so that a phenomenologically viable realization of inflation might be possible in this class of models.

Variational ansätze are a cornerstone of quantum many-body physics, providing compact approximations to complex ground states using finite resources. Recent quantum-technology advances have introduced a new class based on layered parameterized evolutions. Assessing whether they can represent critical ground states is challenging: correlations span all length scales, while finite circuit depth limits how far they extend. Building on finite-resource scaling from tensor networks, we assign each ansatz an emergent correlation length $\xi_D$, the longest range over which it faithfully captures critical correlations. Its growth with refinement parameter $D$, $\xi_D \propto D^\kappa$, defines an exponent $\kappa$ measuring how efficiently an architecture converts resources into long-distance correlations. Applying this framework to the critical transverse-field Ising model, with $D$ the circuit depth of parameterized evolutions, we compare ansätze with nearest-neighbor and long-range generators, and layers where generators act separately or combined. All ansätze are compatible with algebraic growth, but fitted exponents range from $\kappa\simeq1$ to $\kappa\simeq3$. Exponential interactions give the largest exponents, while power-law interactions stay close to nearest-neighbor behavior, showing long-range support alone gives no scaling advantage. Combined-generator layers generally outperform separable ones, so layer organization matters alongside interaction range. Finally, a quasiparticle analysis shows finite depth leaves an unresolved window of width $\xi_D^{-1}$ around the low-energy modes responsible for long-distance correlations. The emergent correlation length thus acts as an infrared resolution scale, providing a benchmark for critical-state preparation and a guide for designing resource-efficient variational architectures.

This paper presents the construction of the supersymmetric (SUSY) deformed version of the time dependent metric that describes the interior of the Schwarzschild BH. First, the noncommutative bosonic model is constructed by inducing the deformation in the minisuperspace coordinates and the associated canonical momentum. Following the methods of SUSY quantum mechanics, the supercharges of the deformed models are constructed and the deformed SUSY Wheeler-DeWitt equation is obtained. The classical dynamics are also obtained using the WKB approximation, we find the classical solutions and the conditions to satisfy the Hamiltonian constraint for both the SUSY and bosonic cases. Finally, the effects of the deformation in the context of deformed phase space cosmology and black holes are discussed.

We study four-dimensional Euclidean Nambu-Goto embeddings in eight dimensions in the presence of the Spin(7)-invariant four-form constructed from octonionic structure constants. A broad class of holomorphic maps is shown by direct substitution to satisfy the nonlinear Nambu-Goto Euler-Lagrange equations. For a compatible Spin(7) structure these same embeddings satisfy the Cayley calibration condition. The calculation therefore gives a discrete octonionic selection rule for the relative orientation of an exact Nambu-Goto 4-surface and the Spin(7) structure of the target.

Near the core of an EFT string in a 4d $\mathcal{N}=1$ theory, the scalars are dynamically driven to infinite field distance and a tower of states becomes light, with mass scaling with the string tension in Planck units as $m^2\sim \mathcal{T}^{\,w}$. According to the Integral Scaling Conjecture, $w$ takes only values 1, 2 and 3. In this paper, we examine how this conjecture can follow from the brane-taxonomy rules associated with the Emergent String Conjecture. In this context, we classify the relevant types of duality frames into 74 classes, identify which lattice sites can be relevant EFT candidates, and exhaustively test integral scaling for all of these candidates. We find that it holds with $w\leq 3$ for all the leading towers and also for the subleading towers below the species scale (up to half-integral subtleties that also appear in top-down examples). We further find evidence that the oscillator modes of EFT string candidates generate the lattices of particles and strings. Moreover, $w=1$ implies a perturbative string limit, but the converse is not true. We compare our classification with concrete type IIA, F-theory and M-theory compactifications.

In this work, we study the effective potential at one loop for the Kalb-Ramond scalar electrodynamics. The model is based on a complex scalar field coupled to the electromagnetic field as usual, and also to the Kalb-Ramond field through the dual vector associated with the strength tensor of the $2$-form gauge field. There is an additional topological coupling of the electromagnetic field and the Kalb-Ramond field. The quantum corrections generated by the Kalb-Ramond sector are computed using dimensional regularization, and the ultraviolet divergences are removed by introducing the appropriate counterterms, leading to a finite renormalized effective potential. We find that the effective potential at one-loop generates terms of the form $\phi^6$, which is not present in the original bare Lagrangian. As a result, we introduced new counter terms to eliminate such divergences. The theory thus considered is not closed under renormalization.

The dilaton is the hypothetical scalar particle associated with spontaneous breaking of approximate scale invariance. It has been predicted to arise dynamically, as a bound state, in special extensions of the standard model of particle physics based on composite dynamics. In confining gauge theories, generic arguments suggest that the scale of explicit symmetry breaking coincides with the confinement scale, that governs also its spontaneous breaking, by setting the size of all the condensates, as well as the masses of bound states and their excitations. Whether a light dilaton can nevertheless exist in such a context is an open question in quantum field theory, answering which has potentially transformative implications from a conceptual viewpoint, besides having striking phenomenological ramifications. It has been suggested that the mass of the dilaton might be suppressed, in respect to the confinement scale, in the special case in which the underlying strongly coupled dynamics undergoes a zero-temperature (weak) phase transition. Identifying the special conditions under which this happens is the subject of ongoing investigations. A dedicated programme of exploration, carried out within the context of gauge-gravity dualities (holography), has been set up to test the viability of this mechanism. We review the relevant technology within holography, and the status of such a programme, by comparing results obtained in a survey of explicit examples. We do so both within the bottom-up, simplified version of gauge-gravity dualities, but also within the more refined, and complete, top-down approach to holography, in which the gravity theory is known to have a more fundamental origin. We highlight the first examples of confining theories in which a parametrically light holographic dilaton forms as a bound state in a region of parameter space in proximity to a critical point of the field theory.

Entanglement through interfaces has attracted considerable attention in 2d conformal field theory (CFT). However, it is known that field-theoretic predictions based on the existing framework are in general incompatible with numerical results [1-4]. A new framework for entanglement through topological defects was recently proposed in [5]. It provides a general description of entanglement through topological defects and successfully reproduces the numerical results for the Ising model in all tested cases and regimes. The key insight is that the relevant quantum correlations are encoded in twisted states, allowing for the construction of the full reduced density matrix (RDM). In this work we pursue two objectives. First, we provide new examples by studying defects in the free boson CFT. Second, we extend the framework to topological interfaces connecting two, possibly distinct, CFTs. Of particular interest are interfaces relating dual theories. We show that the reduced density matrix for a duality interface is the projection of the vacuum reduced density matrix onto a single symmetry sector, closely paralleling the framework of symmetry resolution. Unlike symmetry resolution, however, the projection is imposed by the physical interface itself, demonstrating that duality interfaces reflect quantum correlations back into the entangling interval. We establish this mechanism for diagonal and non-diagonal rational CFTs as well as the free boson CFT. Relative entropy allows us to quantify the distinguishability of the duality interface RDM from the vacuum RDM.

It was proposed that extra dimensions can acquire large size by higher dimensional inflation connecting two large hierarchies in particle physics and cosmology, namely the weakness of the actual gravitational force to the largeness of the observable Universe, in terms of one fundamental scale. This proposal is consistent with the observed approximate scale invariant power spectrum of primordial density perturbations only for one or two extra dimensions of around the micron size. While a cosmological history connecting the period of higher dimensional inflation to the beginning of the standard cosmology has recently been studied, we investigate here the TransPlanckian Censorship Conjecture in that context and show that it drastically constrains the parameter space of the model.

We investigate the spontaneous scalarization of brane-localized charged black holes, focusing on the role of quantum-enhanced tachyonic instabilities. By solving the coupled bulk-brane equations numerically within the Einstein-DeTurck formulation, we construct fully backreacted static black hole solutions and map the system from the semi-classical limit to the strongly coupled quantum-dominated regime. We demonstrate that the holographic quantum effects, parameterized by $\kappa$, significantly modify the background geometry. Stability analysis, conducted via both effective potential diagnostics and quasinormal mode calculations, confirms that this geometric deformation deepens the negative well of the effective potential, thereby triggering a tachyonic instability. Integrating these results, we establish the global phase diagram of spontaneous scalarization in the $T_h/\mu-\kappa$ parameter space. The results reveal that these quantum-enhanced instabilities promote scalarization by substantially raising the critical temperature, providing a clear quantitative signature of quantum effects on black hole hair formation.

This paper is a bottom up attempt to incorporate the standard model and general relativity in a unique quantum field theory. The tentative model presented here in particular is free of chiral gauge and gravitational anomalies that appear in the divergence of currents, and in the divergence and trace of the energy-momentum tensor when the SM matter couples to gravity. The fermion spectrum is composed of two multiplets, the SM (left) multiplet and a mirror copy (right) with opposite handedness. The right multiplet is interpreted as describing the dark matter world. The natural symmetry of the theory is enlarged to incorporate also Weyl invariance, by introducing one or more dilaton fields. After the cosmological and theoretical motivations, the necessary formalism is introduced for algebraic renormalization: gauge fixings, ghosts, propagators and vertices and their interplay in guaranteeing the conditions for convergence of the subtracted amplitudes according to the BPHZL scheme, the Slavnov-Taylor identity and the relevant enlarged BRST symmetry. The corresponding (conformal) cohomology is analyzed and found to be trivial: there are no non-trivial even trace anomalies in theories with dilatons, but there are plenty of trivial ones, which require corresponding counterterms in the effective action. It is shown that such counterterms can play an important role in freeing the theory of unphysical particles.

The properties of hadronic resonances at finite temperature constitute an important probe of the thermal QCD medium. In this work we use the concept of thermoparticles, which characterise thermally-modified but stable particle-like states, to define the notion of two-particle scattering at finite temperature, and establish a unitarity relation for the thermal scattering amplitude. We derive a finite-temperature generalisation of the vacuum two-particle quantisation condition via a skeleton expansion of the finite-volume correlation function. Solving this condition at the finite-volume energy levels of the system constrains the form of the thermal scattering amplitude, and hence the properties of resonances. In contrast to the vacuum case, the kinematic function containing the leading finite-volume corrections is finite at all energies, reflecting the fact that thermoparticles have broadened spectral peaks due to their interactions with the thermal medium. Since all lattice simulations involve a finite temporal extent, our approach can also be used to study finite-temporal size effects in vacuum analyses.

We construct numerically two families of static five-dimensional Lorentzian metrics, solutions of vacuum Einstein equations with a negative cosmological constant, one with and one without a black hole region, with a metric at sections of conformal infinity which is conformal to any squashed three-dimensional sphere.

Here, we investigate the observational viability of fractional power law inflationary potentials, $V(\varphi) \propto \varphi^n$ ($n=$ 1/3, 2/5, 2/3), within the effective framework of Loop Quantum Cosmology (LQC) incorporating inverse volume corrections. By employing LQC modifications to the background dynamics and cosmological perturbation equations in the semi-classical regime, we analytically derive the scalar spectral index $n_{\rm s}$ and the tensor-to-scalar ratio $r$. These theoretical predictions are confronted with the latest high precision joint observational constraints, including ACT DR6, Planck 2018, DESI BAO, and BICEP/Keck datasets (P-ACT-LB-BK18). While steeper classical power law models are in severe tension with modern data, our results demonstrate that the inclusion of LQC inverse volume effects induces a prominent negative shift in $n_{\rm s}$. Consequently, for specific viable ranges of the quantum geometric parameters ($\sigma$ and $\delta$), the theoretical predictions are translated horizontally across the $r-n_{\rm s}$ plane. This mechanism successfully steers classically disfavored models back into the tightly constrained 68% and 95% CLs, significantly improving their consistency with precision cosmological data.

In this article, we discuss some supersymmetric probe D5 brane solutions embedded in a type 2b supergravity background solution obtained by deforming the global $AdS_5 \times S^5$ spacetime. The D5 brane solution of interest has a non-compact worldvolume, and when it is placed alongside overlapping with an anti-$\overline{\text{D5}}$ solution, the combination is dual to a codimension-1 defect of the boundary $SYM$ theory. The dual defect becomes a topological symmetry defect of a $U(1)$ $0$-form global symmetry if we move the profile of the probe D5 more towards the boundary of the bulk spacetime, resulting in a U-shaped profile hanging from the boundary. We show how the hanging D5 brane can be used holographically to measure the $U(1)$ global symmetry charge of the heavy determinant operators in the SYM theory by moving them across dual giant graviton D3 branes in the bulk spacetime.

We investigate static, spherically symmetric charged black holes in Einstein gravity coupled to Euler–Heisenberg (EH) nonlinear electrodynamics, including purely electric, purely magnetic, and dyonic configurations. Rather than adopting the Hamiltonian formulation based on the auxiliary electromagnetic invariant $\mathcal{P}$, we work directly with the physical electromagnetic invariant $\mathcal{F}$ in the Einstein-Euler–Heisenberg Lagrangian, thereby describing all charged configurations without introducing auxiliary variables. Within this approach, we derive an exact analytical solution for the purely electric case, recover the purely magnetic solution directly from the field equations, and construct the dyonic solutions numerically. We systematically study the horizon structure, causal properties, and thermodynamics of these solutions. While the purely electric branch exhibits the familiar Reissner–Nordström horizon structure, the purely magnetic branch naturally admits a novel three-horizon configuration consisting of one event horizon and two inner horizons. The dyonic solutions continuously interpolate between the electric and magnetic limits and exhibit either one- or three-horizon configurations, depending on the magnetic-to-electric charge ratio and the EH coupling. We further show that the EH nonlinear interaction significantly modifies the horizon structure and thermodynamic properties of charged black holes while leaving the central curvature singularity unresolved. These results demonstrate that EH nonlinear electrodynamics gives rise to qualitatively new causal structures beyond Einstein–Maxwell theory.

We derive relativistic resistive magnetohydrodynamics framework for a two-component ultrarelativistic plasma of massless, oppositely charged particles directly from the Boltzmann-Vlasov equation using the 14-moment approximation. The resulting second-order equations couple the net-charge diffusion current to the shear-stress tensor through the electric field, with all transport coefficients given in closed microscopic form. In the homogeneous limit, the charge-current dynamics is well described by relaxation-type Ohm's law for moderate field strengths, while large viscosity drives the system into an underdamped oscillatory regime absent from the standard Israel-Stewart formulation. Most strikingly, a purely electric field generates sizable momentum anisotropy even without any underlying flow gradient. Under Bjorken expansion this field-induced anisotropy persists but becomes subleading to the hydrodynamic expansion source.

We investigate traversable wormholes supported by Casimir vacuum energy with second-order generalized uncertainty principle (GUP) corrections. For two representative GUP models, we derive higher-order corrections to the Casimir energy and construct exact wormhole solutions in general relativity. The resulting geometries satisfy the throat, flare-out, and asymptotic-flatness conditions. Higher-order corrections modify the wormhole mass and reduce the exotic matter required, although the null and weak energy conditions remain violated near the throat. We further analyze weak gravitational lensing and gravitational-wave echoes, finding model-dependent signatures that may distinguish different GUP realizations. By relating the dimensionless parameter used in the solutions to the conventional phenomenological GUP parameter, we show that its physical interpretation depends strongly on the throat radius. Most current experimental bounds favor near-Planckian throats for appreciable GUP corrections, while macroscopic throats generally require much weaker corrections. These results provide a framework for confronting GUP-corrected Casimir wormholes with laboratory constraints and astrophysical observations.

In our previous paper [1], we presented the application of Moonshine to the flavor physics based on the work of Cohn and Deutsch [2] and Bagger and West. Conway and S. Norton [3] and T.Eguchi, H.Ooguri and Y.Tachikawa[4]. We present here the extension of our previous paper [1] by including the supersymmetry and the modular symmetry. We calculate all the lepton masses and the quark masses and their super partner masses by using the one input particle mass for each family. The two valued modular function is defined in equation(7). We define the two valued modular function of degree K in equation (7). We use K = 1 two valued modular function for the charged leptons and k = 2 two valued modular function for the neutrino and for the up quarks and k = 3 two valued modular function for the down quarks. We emphasize that we have three particle masses which can be measured by the existing accelerators such as KEK B factory or CERN LHC. One is super electron mass "Me,s =847 MeV" which is slightly lower than the proton mass. The Super d, s and b quark masses are 0 GeV, 5.56 GeV, and 2193.4 GeV. Super down quark mass is 0 and super strange quark mass can be measured both in KEKB and in CERN LHC. The super bottom quark mass can be measured only in LHC.

We study the thermodynamic and dynamical properties of static, spherically symmetric BHs in Einstein-Maxwell theory modified by a non-minimal $\ln(R)F^{2}$ coupling. The Hawking temperature follows from the Hamilton-Jacobi form of the fermionic tunnelling method for spin-$\tfrac12$ particles, and it carries scale-dependent logarithmic corrections. We then analyze the propagation of massless Dirac fields, compute the quasinormal-mode (QNM) spectrum with the third-order WKB approximation, and read off a quality factor whose balance between oscillation and damping depends on the logarithmic coupling in a mode-dependent way. Moving outward from the horizon, we work out the transmission of the fermionic field and its Hawking emission, and we solve the null and timelike geodesic problems to obtain the photon sphere, the shadow radius, the innermost stable circular orbit (ISCO), the associated zoom-whirl bound orbits, and the orbital and epicyclic frequencies that set the twin-peak quasiperiodic-oscillation (QPO) ratio. A photon-sphere reading of the eikonal QNM frequencies ties the geodesic sector back to the field perturbations. On the thermodynamic side, we build the phase space with quantum-geometric corrections through the Barrow entropy, and we characterize the global phase structure with the topological method, where the winding numbers of the off-shell free energy are governed by the interplay of the fractal Barrow deformation, the electric charge, and the logarithmic coupling. We find that the effective pressure vanishes exactly on the topological defect line, which links the pressure sign to the local stability of each branch.

We develop a local and covariant framework for constraining the evolution of generalized entropy along null horizons, combining classical geometric methods with constraints from quantum field theory. Building on the quantum focusing conjecture (QFC), which restricts entropy evolution along null directions, we derive a Raychaudhuri-type differential inequality for the generalized expansion that makes its local dependence on expansion and shear explicit. The resulting relation, $\frac{d\Theta}{d\lambda} \le -\theta \Theta + \tfrac{1}{2}\theta^2 - \sigma^2$, reveals a direct interplay between expansion and shear in controlling entropy flow: shear contributes negatively and yields a monotonic suppression of the generalized expansion in shear-dominated regimes, while expansion provides a competing geometric source term. This structure provides a local geometric formulation consistent with the QFC and clarifies its interpretation as a constraint on entropy evolution. We further show that quantum extremal surfaces correspond to configurations characterized by $\Theta=0$, whose local stability properties are governed by the same geometric data. In addition, we derive a bound on the exponential separation of nearby null generators, indicating that the same combination of expansion and shear also controls geometric instability. Our results provide a local geometric refinement of entropy bounds in semiclassical gravity and establish a direct connection between null geometry, quantum energy conditions, and entropy flow, offering a local geometric perspective on horizon thermodynamics beyond global formulations.

Recent results demonstrate that there exists a sharp, Page-like transition for the complexity of subsystems of Haar-random states as their fractional subsystem size surpasses one half. They further demonstrate that this transition also occurs for the holographic complexity of boundary subregions of eternal AdS black holes, assuming the Complexity$=$Volume (CV) proposal for subregions. We interpret this transition as a crossover from spectrum-dominated to basis-dominated subsystem complexity, reflecting the breakdown of approximate thermality beyond half-system size. We then apply this reasoning to an evaporating AdS black hole coupled to a bath, modeled by a quantum circuit undergoing random evolution on an interior subsystem of diminishing size. Using the basis-spectrum decomposition of subsystem complexity, we argue for a similar Page-like transition in the radiation complexity. We then show, using CV for subregions, that the same transition appears in the holographic complexity of the radiation subsystem through the emergence of an island, whose volume gives the dominant contribution. We argue that the island volume contribution resolves an apparent complexity paradox analogous to the information paradox.

Recent work has constructed higher-dimensional analogs of non-invertible symmetries similar to 1+1d Kramers-Wannier duality. Although their continuum descriptions often treat purely gravitational topological terms as inessential counterterms, these terms can have an essential lattice manifestation: they distinguish states prepared by finite-depth quantum circuits (FDQCs) from those entangled by nontrivial quantum cellular automata (QCAs). Motivated by this mismatch, we show that QCAs associated with gravitational topological responses arise in several related settings: (1) lattice realizations of projective $\mathrm{SL}(2,\mathbb{Z}_N)$ relations generated by topological operations on symmetries; (2) squares of dualities that generalize the relation between fermionization and Kramers-Wannier duality; (3) lattice implementations of QCAs through higher-form gauging; and (4) invertible phases protected by generalized time-reversal symmetries. We derive new projective $\mathrm{SL}(2,\mathbb{Z}_N)$ relations whose projective phases are gravitational topological responses constructed from Stiefel-Whitney classes. We furthermore give a general protocol for preparing the associated QCA-entangled states using finite-depth unitary circuits, measurements, and error correction. These results unify the study of gravitational topological responses in field theories, higher dimensional dualities, and quantum cellular automata.