Papers

We obtain the action for the chiral Carroll string moving in a curved string-Carroll target spacetime from a Carroll expansion, in powers of the speed of light $c$, of the action for the relativistic closed bosonic string. Applying this setup to a classical closed bosonic string approaching the $4$-dimensional Schwarzschild black hole, we study the dynamics of the string when it behaves as a chiral Carroll string with the near-horizon string-Carroll expanded geometry as the target spacetime. We find that the chiral Carroll string can have either left-moving or right-moving fluctuations on the horizon, while exhibiting a non-trivial motion in the Rindler spacetime which depends on these horizon fluctuations.

Recent DESI baryon acoustic oscillation measurements, combined with cosmic microwave background and type-Ia supernova data, suggest that dark energy may evolve with cosmic time. Along a cosmological background, an evolving dark-energy density can be expressed locally as a function of a monotonic curvature invariant, motivating an effective curvature-dependent cosmological term. Moreover, quantum field theory in curved spacetime and approaches to quantum gravity with running gravitational couplings provide complementary motivations for exploring such a term. Here we study how the phenomenology of nonsingular rotating black holes embedded in a Universe dominated by dark energy can differ substantially from that of the Kerr and Kerr–de Sitter geometries. The problem is directly formulated in phase space using a null geodesic super-Hamiltonian and a Mino-type parameter. The shadows of the black holes are calculated by backward ray tracing from a zero-angular-momentum observer. We define and analyze a comprehensive set of standard shadow observables, characterizing the size, shape, and displacement of the shadow. We show that the area of the shadow and its vertical diameter provide particularly clear signatures of a running cosmological term. In this way, joint analyses of multiple strong-field observables and of several black holes with different masses and spins could provide a realistic route to tightly constraining, or potentially measuring, the effective regularization scale behind the running of the cosmological term and statistically distinguishing the non-singular black hole geometry from Kerr/Kerr-dS solutions.

Inflation driven purely by the quantum running of the curvature-squared couplings of quadratic gravity was shown to accommodate the high scalar tilt favored by recent cosmic microwave background observations, starting from a Euclidean four-sphere at a maximum of the running $R^2$ coupling. That maximum exists only in one renormalization scheme, and is not stationary once the Euler trace anomaly is included. We show that the standard one-loop running, with the usually neglected Gauss–Bonnet coefficient retained, recovers the missing de Sitter state: the Euler running balances the scale dependence of the $R^2$ term at a unique coupling ratio, giving a de Sitter solution that is stationary for the gravitational constraint and for the compact Euclidean action alike, and whose scalaron potential is an extremely flat hilltop ($m^2/H^2\simeq-5\times10^{-10}$) joined to an inverse-linear inflationary plateau. The last $N_*\simeq50$–$60$ $e$-folds are scheme independent, with scalar tilt $n_s\simeq1-4/(3N_*)$, while the tensor-to-scalar ratio, $r$, is set by the number of matter fields that enhance the running. The current tensor bound excludes pure gravity and sets a minimum matter content, some $4\times10^6$ conformally coupled scalars or $3\times10^5$ vectors—$2.6$ times fewer than the momentum-induced scheme requires—while one-loop control to the end of inflation sets a maximum about ten times higher. Across that window the model predicts $r\gtrsim0.008$ with $0.973\lesssim n_s\lesssim0.978$, within reach of upcoming CMB polarization surveys.

The constraints for the effective local gauge groups stemming from the causal action principle for causal fermion systems are reviewed. The constraint which are quadratic in the gauge potentials (coming from the so-called bilinear logarithmic terms) are shown to make a connection between the structures of Lie algebras and Clifford algebras. This connection is worked out systematically starting from general chiral potentials corresponding to the gauge group $\mathrm{U}(N) \times \mathrm{U}(N)$. The general results are illustrated in various examples.

We present a theoretical proposal for measuring correlation functions in a quantum field system based on the use of quantum quenches. Using the examples of massive and massless scalar field theories, we show that a short-term perturbation of the system leads to a dependence of the further evolution of the average field on the initial state's correlation functions. Considering two types of perturbations, namely local and nonlocal quenches, we show which correlation functions can be measured in each of these cases. The proposed procedure can be applied to study non-Gaussian correlations.

A composite soliton can lose its binding through a change in the ordering of the vacua that fill its interior and its exterior, while the quantum correction to its mass stays small. We show this in the non-degenerate double sine-Gordon model, normal ordered at the meson mass of the primary vacuum. At one loop the central secondary vacuum becomes the true vacuum at a coupling of order the classical splitting of the vacua, because the quantum tension of a string of secondary vacuum carries the logarithm of the meson-mass ratio. Matrix-product-state calculations for $n=4$ confirm the inversion, extrapolate to the continuum, and are reproduced by the Gaussian effective potential. Finite-chain calculations at two lattice spacings show the string joining the two halves of the $Q=4$ multi-kink lengthening as its tension falls and, past the crossing, filling the box, with the slope of the energy in the box length equal to the vacuum-energy difference and the correction to the mass still under a tenth of the classical value.

The effective-field-theory interpretation of generalized uncertainty principle (GUP) deformations does not by itself establish whether their tree-level operator content is closed under renormalization. We investigate this question in massless GUP-deformed quantum electrodynamics at one loop and to first order in the deformation parameter. We compute the ultraviolet divergences of the relevant Green functions and determine the counterterm structure. Our central result is that, after eliminating redundant operators, renormalization requires only one independent physical counterterm beyond those associated with the tree-level theory: an axial-axial four-fermion interaction. The original deformation therefore admits a minimal radiative completion at this order. We derive the leading logarithmic running of the induced Wilson coefficient and discuss its operator-level correspondence with the contact interaction arising in Einstein-Cartan gravity.

From a holographic perspective, we formulate an exact finite-duration covariance framework that resolves chirality in the AdS/CFT correspondence. In a rotating BTZ black hole spacetime, relative motion between two boundary controls converts sum-frequency matching on the compact boundary cylinder into discrete velocity resonances indexed by the angular momentum of the scalar field. Because the complete real-control covariance also contains difference-frequency sectors, a two-setting phase cycle with a common switching window cancels them exactly at finite duration and reconstructs the resonant pair contribution from complete positive-semidefinite covariance matrices. For an isolated angular mode, reconstructed pair responses at opposite resonance velocities sample the boundary spectrum at opposite angular momentum and a common control-selected frequency. Their normalized contrast cancels reflection-symmetric control factors and the state-independent operator normalization, yielding a finite-linewidth estimator of the reflected-mode BTZ contrast. Under the stated smoothness and moment conditions, common centered even narrowing windows give a bias beginning at quadratic order in linewidth. A real-projection leakage bound controls contamination from neighboring modes. Long-pulse calculations with the exact BTZ spectrum verify phase-cycle reconstruction and quadratic linewidth scaling. Bath-weighted calculations with exact truncated transfer amplitudes establish convergence to this baseline. Under the default controls, complete-sum contrasts for the first two nonzero angular modes reconstruct the reference-state rotation parameter at fixed mean inverse temperature with subpercent deterministic bias in the untruncated Gaussian limit. The inferred rotation parameter fixes the horizon parameters of the rotating BTZ black hole once the mean inverse temperature and AdS radius are known.

It has long been a puzzle why the nuclear modification factor in relativistic $p$Pb collisions is consistent with unity, while the high-$p_T$ elliptic flow is significantly positive. The latter is traditionally interpreted as path-length-dependent energy loss, whereas the former is consistent with zero energy loss. In this Letter, we propose that even at high $p_T$ a hard parton coalesces with a boosted thermal medium parton whose energy is correlated with the angle-dependent radial flow. We compare this flow for $pp$, $p$Pb, $p$O, OO and PbPb collision systems and conclude in particular that the $p$Pb flow is large and anisotropic. The collective medium pushes out the hard partons, and more so in $p$Pb, or in-plane, than in $pp$ collisions, or out-of-plane. The mechanism qualitatively agrees with experiment and predicts a significantly smaller elliptic flow signal for jets than for hadrons.

The notion of a spatiotemporal quantum state extends the conventional concept of a spatial quantum state to the spatiotemporal domain. Such states are represented by unit-trace operators that encode correlations among quantum events distributed across space and time. In this work, we use the spatiotemporal Kirkwood-Dirac phase space to provide a unified characterization of spatiotemporal quantum states. Spatiotemporal states obtained from Kirkwood-Dirac distributions are generally non-Hermitian and nonnormal; whereas those constructed from Margenau-Hill distributions are Hermitian. We provide a unification via (quasi)probabilistic mixture of Kirkwwod-Dirac spatiotemporal states which encompasses almost all existing formulations of spatiotemporal quantum states. We derive recursive expressions for spatiotemporal states and elucidate the relation between Kirkwood-Dirac nonclassicality and the temporality of spatiotemporal states. We further extend the construction to many-fold correlation functions and establish its connection with out-of-time-ordered correlators (OTOCs). We also develop a more general unifying framework based on (quasi)probabilistic mixture of $s$-parametrized spatiotemporal states and establish their Petz time reversal and application in studying Kubo-Martin-Schwinger (KMS) condition in two-time setting. Finally, we apply this framework to characterize quantum entanglement in spacetime and analyze spatiotemporal entanglement using several complementary entropy measures.

We study a double scale limit of $U(N)_k\times U(N)_{-k}$ ABJM theory, with $N,k\to\infty$ and $N/k^2\to\nu\in(0,\infty)$, at fixed positive total monopole charge $q$. In this limit, the Penrose geometry retains a compact null circle of finite radius, and the sector of monopole charge $q$ carries $q$ units of longitudinal momentum. It is therefore naturally associated with the rank-$q$ BMN matrix model, while $\nu$ fixes its dimensionless coupling. We establish this relation from both gravity and the supersymmetric index. On the gravity side, we take the double scale limit of Hopf quotients of the Donos–Simón half-BPS geometries. The disk carrying the growing background flux becomes an infinite conducting plane, while the remaining finite disks reproduce the Lin–Maldacena electrostatic problem. Their quantized fluxes map directly to the partition data labeling BMN vacua. On the field-theory side, starting from the finite-$N$, finite-$k$ ABJM localization formula, we prove that, at fixed positive monopole charge $q$, the ABJM superconformal index factorizes coefficientwise in the transverse fugacities into a universal neutral contribution and the refined Witten index of the rank-$q$ BMN matrix model, together with the longitudinal momentum weight. The neutral contribution is precisely the limiting zero-monopole-charge index. Dividing by this universal factor therefore isolates the BMN index summed over all its supersymmetric vacua.

The black hole zeroth law asserts the thermal equilibrium of a stationary Killing horizon, yet its status beyond general relativity remains limited. We demonstrate that its validity is not governed by a universal mechanism: distinct gravitational theories enforce constancy of the surface gravity through different horizon-projections of their field equations. In general relativity, $f(R)$-gravity, and Lovelock theories, the zeroth law is known to follow from the mixed (null-transverse) horizon equations. By contrast, we show that in non-Lovelock theories the zeroth law is enforced by qualitatively different mechanisms. In generalized quadratic gravity, for instance, the null-null component of the field equations dictates its validity. Exploiting this novel diagnostic, we obtain the first exact proof of the zeroth law in the broader landscape of higher-curvature gravity, without relying on a perturbative expansion around general relativity. Our result establishes the zeroth law as a sharp probe of the underlying thermodynamic structure of gravity, and points toward a classification of modified theories according to the mechanism responsible for its validity.

We study the insertion of 4d half-BPS line defects into the trace formula proposed by Gaiotto and Kim, which computes the ellipsoid partition function of the 3d topological quantum field theory (TQFT) arising from a 4d $\mathcal{N}=2$ superconformal field theory. This yields a homomorphism to 3d Wilson loops, preserving the fusion algebra of the 4d defects. We also present a systematic algorithm for determining the simple objects of a 3d TQFT in terms of Wilson loops in the UV 3d $\mathcal{N}=2$ abelian Chern-Simons-matter theory. Utilizing supersymmetric localization, we characterize the modular $S$- and $T$-matrices of the TQFT. We apply our algorithm to various 3d TQFTs arising from the trace formula with higher-power monodromy of the $(A_1,G)$ Argyres-Douglas theories.

We investigate the relation between de Sitter entropy and holographic entanglement entropy in higher-curvature gravity and its braneworld realization. Using the canonical formulation of the gravitational action and the Euclidean gravitational path integral, we derive the de Sitter entropy, including contributions from higher-curvature surface terms, and compare it with the holographic entanglement entropy obtained from the corresponding entropy functional. We first consider Gauss-Bonnet gravity and show that the two entropies coincide for static asymptotically de Sitter braneworld spacetimes on the RS II model, while they generally differ for stationary spacetimes. The mismatch in the stationary case arises from an extrinsic-curvature contribution associated with the constant-time surface, which vanishes for static configurations but is generally nonzero for stationary geometries. We then extend the analysis to general Lovelock gravity and show that the agreement between the de Sitter entropy and holographic entanglement entropy persists for static asymptotically de Sitter braneworld spacetimes in the RS II model beyond the Gauss-Bonnet case. We also comment that the same distinction between static and stationary configurations applies to braneworld black holes: the black hole entropy agrees with the holographic entanglement entropy in the static case, while the two generally differ for stationary braneworld black holes. Our results clarify the relation between gravitational and holographic entropies in higher-curvature gravity and provide a broader perspective on holographic correspondence in Lovelock theories and their braneworld realizations.

The ATLAS Collaboration has searched for Higgs-boson decays into a photon and missing transverse momentum using $135~\mathrm{fb}^{-1}$ of Run~3 proton–proton collision data at $\sqrt{s}=13.6~\mathrm{TeV}$. For the benchmark decay $H\to\gamma\gD$ with a massless invisible dark photon, ATLAS reports observed (expected) 95% confidence-level limits of $1.4\%$ ($1.2\%$) on the branching fraction. We reinterpret this search for a massive detector-invisible dark photon with $0\leq m_{\gD}\leq70~\gev$, focusing on Higgs production through gluon–gluon fusion. \audit{The relative signal acceptance, normalized to the massless benchmark, remains nearly unchanged up to $m_{\gD}\simeq40~\gev$, but decreases to $0.888$, $0.736$, and $0.524$ at $50$, $60$, and $70~\gev$, respectively, as the photon-$p_T$ and transverse-mass spectra move toward the analysis thresholds.} Using the published massless gluon–gluon-fusion yield for normalization, we obtain simplified expected (observed) 95% confidence-level limits on $\BR(H\to\gamma\gD)$ from $1.64\%$ ($1.76\%$) at $m_{\gD}=30~\gev$ to $3.50\%$ ($3.75\%$) at $70~\gev$. These results extend the ATLAS interpretation to massive invisible dark photons and quantify the resulting loss of sensitivity at large dark-photon mass.

We investigate the classical double copy of the rotating black-hole geometry induced on the brane in the Randall-Sundrum II scenario. The influence of the five-dimensional bulk is encoded in the effective four-dimensional geometry through a tidal charge, while the metric admits a Kerr-Schild representation over a flat background. We construct the corresponding single and zeroth copies and find that their regular sources are entirely proportional to the tidal charge, whereas the mass-dependent contribution is source-free in the regular region. Comparison with Kerr-Newman reveals a formal correspondence between the tidal charge and the squared electromagnetic charge at the level of the induced geometry and its double copies, despite their different physical origins and the fact that the tidal charge may take either sign. When an electromagnetic field is included on the brane, both contributions enter the low-energy Kerr-Schild geometry and its double copies only through the combination $Q^2+\beta$. These results illustrate how physically distinct brane and bulk contributions can become indistinguishable in the classical double copy of an effective geometry.

We study finite-$N$ coherent-state overlap kernels in multi-matrix BPS sectors of $\mathcal N=4$ super Yang–Mills theory. For commuting coherent-state parameters, the kernel is a Laplace transform of the Haar-pushforward measure on the unistochastic set. After quotienting row- and column-shift redundancies, the nontrivial source is an $(N-1)\times(N-1)$ matrix $D$. On the physical $m$-matrix locus, $D$ is a Gram matrix with $\operatorname{rank}D\leq m$, and the ordinary HCIZ sector is precisely the rank-at-most-one stratum. For $N=3$ we obtain an exact Bessel-integral representation of the first genuinely rank-two kernel. Along the rank-one ray $D=rE_{11}$, $F_N={}_1F_1(1;N;r)$ for arbitrary finite $N$. Using $K_N=\log F_N$ as the reduced Kähler potential, we study a controlled two-matrix embedding of the HCIZ sector and determine its transverse metric, second fundamental form, and Gauss–Codazzi geometry. The embedding is non-totally-geodesic at finite $N$. In the scaling $r=N\rho$, we find \begin{equation} Nh_N\to\min(\rho,1), \qquad \|B\|^2\to2(1-\rho)_+. \end{equation}

We study secondary pairing in the two-flavor color-superconducting (2SC) phase, where the residual ungapped quarks form a same-chirality $J^P=1^+$ condensate driven by an attractive instanton-induced interaction. We determine its symmetry realization, quasiparticle structure, anomaly matching, and low-energy effective theory. The pairing gap is necessarily nodal; in particular, the complex axial state has two point nodes and realizes a spinful relativistic superfluid. This state preserves the full chiral symmetry ${\rm SU}(2)_{\rm L}\times{\rm SU}(2)_{\rm R}$ while breaking the modified baryon-number symmetry ${\rm U}(1)_{\tilde{\rm B}}$ and spatial rotations, with rotations about the nodal axis locked to the condensate phase. This locking gives rise to a Berry term, the Mermin-Ho relation, and a type-B orientational Nambu-Goldstone mode in addition to the superfluid phonon. We also show how anomaly matching is reorganized by secondary pairing: the perturbative mixed ${\rm SU}(2)_{\rm L,R}^2{\rm U}(1)_{\tilde{\rm B}}$ anomaly is realized by a Wess-Zumino coupling of the superfluid phonon, whereas the ${\rm SU}(2)_{\rm L}$ and ${\rm SU}(2)_{\rm R}$ Witten anomalies are carried by the point-node Bogoliubov-de Gennes flavor doublets. The resulting theory provides a concrete dense-QCD realization of a spinful relativistic superfluid with nodal fermions required by anomaly matching.

On a $d$-dimensional, $d\geq 2$, globally hyperbolic spacetime with a timelike boundary $(\mathcal{M},g)$, we investigate the Klein-Gordon equation with Robin boundary conditions. First of all, we prove existence and uniqueness of the advanced and retarded fundamental solutions, discussing in addition their structural properties. Secondly, under the hypothesis of infinitesimal convexity of $\partial\mathcal{M}$ and of local finiteness of boundary reflections for broken null bicharacteristics, we characterize their wavefront set in the interior $\mathring{\mathcal{M}}$, using the propagation of singularities theorem of Melrose and Sjöstrand. In the second part of the paper, we introduce a notion of Robin-Hadamard two-point correlation function as a positive distribution on $\mathcal{M}\times\mathcal{M}$ with prescribed antisymmetric part and singular structure, the latter being characterized in terms of its wavefront set. We complement this definition with a local Hadamard form. Up to a smooth remainder, this consists of the standard directed Hadamard parametrix together with additional contributions associated with the reflected null rays. Their coefficients are determined by transport equations supplemented by Robin matching conditions at the boundary. The construction applies to an arbitrary, but finite number of reflections. We prove that this local formulation is equivalent to the wavefront set condition, thereby establishing a counterpart of Radzikowski's theorem in the presence of a timelike boundary. Finally, starting from the ground state on suitable static backgrounds and using a deformation argument, we prove existence of Robin-Hadamard two-point correlation functions on the class of spacetimes considered.

We investigate field-induced excitation production from the unit-filled Mott background of a one-dimensional dipole-conserving Bose–Hubbard chain driven by a periodic quadratic potential, realizing a time-dependent rank-two electric field. Unlike protocols that manipulate pre-existing dipolar or fractonic excitations, we address their production from an initially Mott-like state without prepared dipolar or fractonic excitations. A single correlated hop directly nucleates the compact $|030\rangle$ configuration at the atomic energy $3U$, while a lower manifold derived from $2U$ contains spatially resolved dipole–antidipole configurations. Exact diagonalization shows that finite hopping turns this lower manifold into a dispersive band whose finite-chain edge lies substantially below the compact $3U$ scale. Despite this lower energetic edge, its normalized odd-harmonic spectral weight is perturbatively suppressed as $(J/U)^2$, reflecting virtual hybridization of the initial and final eigenstates. A consistent second-order treatment of the $|1111\rangle\leftrightarrow|0220\rangle$ channel includes diagonal self-energy shifts and predicts a weak-field resonance displacement confirmed by exact time evolution. Extended-chain dynamics shows genuine dipole–antidipole separation together with redistribution into higher-energy many-body sectors. The resulting mechanism provides a condensed-matter analogue of multiphoton dynamical Schwinger production in which exact dipole conservation replaces mobile opposite charges by mobile opposite dipoles, while isolated fractonic charges remain immobile.

The exact behaviour of the enveloppes of the single-time and two-time correlators is found for the voter model on a fractal substrate, with nearest-neighbour interactions. Herein the geometry of the fractal substrate is described by its non-integer geometric fractal dimension $d_f$, and its topology and diffusive transport by the distinct spectral dimension $d_s$. On the level of the equations of motion of the correlators this can be modelled by considering a space-dependent diffusion constant ${\cal D}(r)\sim r^{-\theta}$ which implies the spectral index $\theta$, itself a function of $d_f$ and $d_s$. With a scaling ansatz, the generic phenomenology of ageing is confirmed and the dynamic exponent ${z}=2+\theta$ and the autocorrelation exponent $\lambda=d_f$ are derived. The explicitly found dynamic scaling functions are shown to depend only on the spectral dimension $d_s$. The decay of the enveloppe of the density of active interfaces with time is described by the exponent $\alpha=1-d_s/2$ for $d_s<2$, confirming the results of preexisting numerical simulations.

In this paper, we study Abelian T-duality of the string charge density/bit threads correspondence in ten-dimensional Type II supergravity. T-duality along the common compact circle maps the Type IIB F1-NS5-P background to a Type IIA P-NS5-F1 background with the winding and momentum charges exchanged. The radial F1 source remains an F1 source, and its projected charge density gives a bit-thread flow whose maximal flux reproduces the black hole entropy. The same duality maps D1-D5-P to D0-D4-F1. In this case, a radial D1 source becomes a D2 source wrapped on the dual circle. Contracting the resulting spatial bivector with the normalized closed one-form on that circle gives a conserved effective radial flow whose maximal flux again reproduces the entropy. Although the local metrics, dilatons, source currents, and flow norms change, the dilaton-weighted transverse area density and the integrated maximal flux are invariant. These results provide a nontrivial T-duality test of the correspondence and extend it from string currents to wrapped-brane currents that reduce to string-like flows.

We investigate the spin-curvature interaction for a massive spin-1/2 quantum particle in a slowly rotating black hole spacetime. In contrast to the flat Minkowski space, the curved spacetime introduces non-trivial spin connections into the Dirac equation due to the direct curvature-spin interaction. The force arising from this non-trivial spin-curvature coupling makes the particle deviate from its geodesics. We first calculate the tetrads in the co-moving frame of the particle in the slowly rotating black hole background. We then compute the components of the relativistic quantum force, arising from the spin-curvature interaction, using these co-moving tetrads up to linear order in the rotation parameter ($a$) of the black hole. The procedure of computing the force is based on the WKB approximation and the Gordon decomposition method for the Dirac probability four current. Our results show that the rotation parameter modifies the magnitude of the force by introducing a term that decays more rapidly with radial distance than the force magnitude in a static spherically symmetric Schwarzschild black hole spacetime.

In this paper we propose a universal way to define multivariate orthogonal polynomials for the positive branch of WLZZ matrix models. This allows us to generalize from the Gaussian case, previously considered in the literature, the strict superintegrability property and the Miwa deformation formulas.

We establish a saddle-order proposition for the ensemble-averaged generalized free energy in reduced Euclidean black hole ensembles. Under regularity and stability assumptions, the leading fluctuation contribution is determined by the order of the first stabilizing term around the dominant saddle. An ordinary critical point is governed by a quartic soft mode, giving a quarter-temperature contribution instead of the familiar half-temperature Gaussian result. We verify this analytically for four-dimensional RN-AdS and Kerr-AdS black holes and map their thermodynamic controls to a common quartic normal form, whose scaling function connects the critical and Gaussian regimes along the zero-field one-well direction. The proposition also extends to coupled collective modes with weighted-homogeneous leading potentials. These results provide a unified description of reduced-ensemble fluctuations through black hole criticality.

We present a gate-based quantum computing solution of the homogeneous Bethe-Salpeter equation (hBSE) for the bound state of two massive relativistic scalar particles interacting via ladder-approximation scalar exchange. After Wick rotation to Euclidean space and O(4) S-wave partial-wave projection, the hBSE is reduced to a symmetric matrix eigenvalue problem of dimension N = 2^n. We decompose the resulting Hamiltonian into a sum of n-qubit Pauli operators and solve it with the Variational Quantum Eigensolver (VQE) using a Matrix Product State (MPS) tensor-network ansatz. For N=16 (n=4 qubits), the VQE recovers the maximum eigenvalue - which encodes the minimum coupling constant for binding - to better than 1 % mean relative error compared to classical diagonalization. Entanglement analysis of the BSE amplitude shows low, area-law-like entanglement over the tested sizes, which motivates the MPS ansatz. A critical analysis of three independent barriers - exponential Pauli overhead, approximately size-independent low entanglement, and decreasing VQE gradient scales for the tested ansatz, consistent with generic barren-plateau concerns at larger n - reveals that the specific problem studied here lies in a classically tractable regime: over the tested range it is well described by low-bond-dimension tensor networks and efficiently handled by MPS/Lanczos methods. This negative result provides, to our knowledge, the first entanglement quantification of the BSE amplitude in qubit encoding, establishes the Pauli Hamiltonian framework for future BSE variants, and identifies 2D Minkowski-space BSE, N-body bound states, and non-ladder kernels as physically motivated extensions where genuine quantum advantage may become plausible.

We study continuous scalar-hair bifurcations from stationary black holes with a nonextremal Cauchy horizon. Although the exterior deformation vanishes at criticality, the critical zero mode generically develops a logarithmic branch at the reference Cauchy horizon, producing a nonuniform critical limit. We show that the coefficient of this logarithm in the scalar perturbation, together with local Cauchy-horizon data, determines the exponential collapse rate of the Einstein-Rosen bridge. If the post-collapse geometry evolves into a Kasner regime, the boundary order-parameter scaling $O\propto|\lambda-\lambda_c|^\beta$ further implies $ 1-p_t\propto|\lambda-\lambda_c|^{2\beta}. $ Crucially, zero-mode matching fixes both the critical exponents and the associated amplitudes, without any fit to the nonlinear interior. We illustrate this mechanism in the transition from rotating BTZ to hairy rotating black holes. For scalarized RN-AdS$_4$ black branes, we quantitatively verify the predicted Kasner scaling using fully nonlinear numerical solutions. At low temperature, two charged models with identical linear critical data instead approach different infrared endpoints, yielding respectively power-law and inverse-logarithmic Kasner scaling. Thus interiors near a finite-temperature bifurcation are controlled by zero-mode transmission, whereas low temperature scaling is governed by the nonlinear infrared completion.

In this paper, we study Einstein-Dirac system based on a Dirac fermion coupled with a nonlinear chiral field on static spherically symmetric spacetime. Gravitational effects on the dynamical mass of fermions are examined. The chiral quark soliton model (CQSM) originally was a model of hadron inspired by the low-energy regime of large-$N_\textrm{c}$ QCD, realizing localized fermions with the full inclusion of the Dirac-sea, which is derived from a regularized one-fermion loop. We extend the CQSM in spherically symmetric curved spacetime and coupled with the Einstein gravity. We successfully solve the CQSM and the Einstein equation self-consistently, and obtain the spectral flow of the fermion energies and also of the ADM mass. The Dirac-sea dilutes the effect of the energy-momentum tensor, which induces an inactive point for the impact of gravity even when the localizing matter exists. The Dirac-sea effect becomes dominant for larger dynamical mass $M\sim \langle\bar{\psi}\psi\rangle$, leading to the emergence of the negative ADM mass.

In this paper, we investigate the relation between the category of 3-crossed modules and the category of Gray-type 4-groups. The notion of a 3-crossed module was first introduced by Arvasi et al., motivated by the question of what kind of algebraic structure completely encodes a homotopy 4-type. On the other hand, from the point of view that higher groups are equivalent to algebraic realizations of higher categories – as exemplified by the relationship between 2-crossed modules and Gray 3-groups established by Sarikaya–Ulualan – it had not been clear how the 3-crossed modules of Arvasi et al. relate to any higher category. In our previous paper, we proposed a new definition of a 3-crossed module and observed that it admits a natural interpretation in terms of higher categories. In this paper, we make this interpretation precise: we introduce a 4-category, which reduces to a semistrict braided monoidal 2-category when restricted to a single object and a single 1-morphism, and prove that the category of our 3-crossed modules is equivalent to the category of Gray 4-groups, defined as single-object versions of this 4-category in which all morphisms are invertible. Furthermore, while Gray 4-groups provide a conceptual framework for 4-dimensional higher structures, they are often computationally intractable. Our equivalence establishes 3-crossed modules as a concrete, group-theoretic calculus for Gray 4-groups, providing a powerful computational tool for studying surface knots, state-sum invariants, and higher gauge theories.

We investigate the phenomenological consequences of a genuine three-body holonomy in a relativistic Dirac system in one spatial dimension. After removing the center-of-mass coordinate, the triple-coincidence point punctures the two-dimensional relative configuration space and permits a nontrivial $U(1)$ winding phase, whereas the pairwise Sakamoto–Munakata–Ino contact interactions give trivial net matching around this point. At fixed intrinsic parity, the six particle-ordering sectors reduce to a three-dimensional cyclic space. A Hermitian $C_3$-invariant effective mass operator admits a Peierls-type realization in which the gauge-invariant phase around the three links equals the three-body holonomy $\theta_3$. Its eigenvalues are $$ M^{[k]}=M_0+2\Delta\cos\!\left(\frac{\theta_3+2\pi k}{3}\right), \qquad k=0,1,2. $$ The holonomy lifts the conjugate-channel degeneracy and can generate a parametrically light branch through cancellation between the common mass and the holonomy-induced shift. We further allow cyclic-symmetry breaking and consider a general Hermitian three-state mass matrix. Exact elimination of two heavy states by the Schur complement yields a low-energy correction containing the rephasing-invariant loop product $\mathrm{Re}(t_{12}t_{23}t_{31})\propto\cos\theta_3$. Thus, even when only one branch is kinematically accessible, its effective mass can retain finite memory of the complete three-state loop. The complementary invariant $\mathrm{Im}(t_{12}t_{23}t_{31})\propto\sin\theta_3$ is phase sensitive but does not alone imply CP violation. The construction provides a low-dimensional phenomenological proof of concept for family-like triplication, mass hierarchy, and infrared memory, rather than a microscopic theory of Standard Model fermion generations.