Papers

We present a formulation of quantum field theory based entirely on real numbers, which we call real quantum field theory (RQFT). The construction is obtained from the standard complex-number formulation by replacing the imaginary unit i with a matrix J throughout all formulas. Here J is the real 2x2 matrix satisfying the condition J^2=-1. This extends the recently developed formulation of real quantum mechanics based on the real Kähler space to systems with infinitely many degrees of freedom. As the basic example, we construct the RQFT for a scalar field. We define a field operator acting on the real Kähler analogue of the bosonic Fock space. This operator satisfies the Klein-Gordon equation and the J-form of canonical commutation relation. To construct the RQFT we develop the corresponding J-calculus. In particular, we introduce the direct and inverse J-Fourier transforms and the associated J-valued distributions. In RQFT, the usual unitarity condition for the complex S-matrix is replaced by the statement that the real scattering operator is both orthogonal and symplectic. The physical observables in RQFT coincide with those of ordinary QFT. Thus RQFT does not change the physical predictions of scalar QFT, but provides an equivalent formulation. We explore the possibility of purely real formulations of the Standard Model of elementary particles. We show that it does admit this formulation and the resulting theory has ortho-symplectic symmetry. The choice of the Standard Model as the testbed for exploring the possibility of purely real formulations is related with the fact it provides a realistic description of all known fundamental particles. The real formulation of the Standard Model naturally suggests a possible exit beyond the Standard Model. In particular, we consider the implications of breaking the J-symmetry as a marker for new physics.

The KP equation is a prototypical $(2+1)$-dimensional integrable PDE. Its soliton solutions are famously parametrized by the Sato Grassmannian. In seminal work, Kodama and Williams made the surprising discovery that the combinatorics of soliton solutions are intimately related to the combinatorics of the totally positive Grassmannian as pioneered by Postnikov. They introduced novel algorithmic methods inspired by polyhedral structures arising from tropical geometry. Soliton solutions to the 2D Toda lattice and the Davey–Stewartson equation, two closely related integrable systems with soliton solutions, are also classified by the Sato Grassmannian. Kodama suggested that the methods of his work with Williams could generalize to these two integrable equations. In this work, we show that this is indeed the case. We derive algorithms to produce contour plots from elements in the totally nonnegative Grassmannian in both cases. In the asymptotic setting, we recover and refine previous work of Biondini and Wang; as well as Biondini, Kireyev and Maruno.

In this work, we investigate the quantum entanglement properties of analog Hawking radiation produced by a moving mirror. Using two detector modes defined through window functions on a quantum field, we quantify the bipartite entanglement established between these modes. Our results reveal that the amount of entanglement accessible to the detectors increases when the mirror follows trajectories with non-monotonic, time-dependent acceleration, which are accompanied by the emission of negative energy flux. This indicates that the negative energy flux acts as a channel through which information can be returned. To substantiate this perspective, we examine how the recovery or reconstruction of the associated partner modes is related to the negative energy flux emitted by the mirror.

Reentrant phase transitions of accelerating anti-de Sitter black holes are known numerically, but their apparent loss at small string tension has lacked an analytic explanation. In the single-string ensemble at fixed pressure, charge, and tension, we solve the unrestricted two-phase Maxwell-turning problem for the charged slowly accelerating C-metric. Elimination forces the two horizon coordinates to coincide and yields a closed one-parameter locus. An exhaustive enumeration of the remaining equilibria establishes global phase selection throughout the physical black-hole sector. The locus exists for $0<\mu<0.202602$, with no positive lower threshold. As $\mu\to0$, the pressure and temperature widths of the reentrant window contract as the fourth and third powers of the tension, while the entropy gap and latent heat diverge. A two-chart blow-up gives a parameter-free limiting profile and identifies thermodynamic-volume inversion as the turning mechanism between two distinct noncritical phases. At a Maxwell boundary with fixed sheet incidence, projective Newton data of the thermodynamic jumps determine the leading coexistence profile. Their positive simple roots fix the turn count, order, and curvature signs; the C-metric realizes the primitive binomial class.

In this paper, we investigate novel classical non-local effects in scalar field theory arising from the presence of external sources and a material boundary. Specifically, we consider a model in which the standard Klein-Gordon field theory is modified by a non-local term. First, we analyze the interaction between stationary field sources modeled as point-like scalar charges. In specific configurations, the resulting interparticle potential reduces to the Cornell form. Then, we examine the model in the presence of a Dirichlet plane, computing both the scalar field propagator and the interaction force between the Dirichlet plane and a point-like scalar charge. Additionally, we demonstrate the failure of the image method in this non-local context and compare our results with those obtained in non-local electrodynamics and in the standard Klein-Gordon field theory.

We propose a general necessary condition for a spinful fermion chain with SU(2) spin-rotation symmetry to be gapped. Specifically, we prove that the expectation value of a properly defined fermionic twisting operator asymptotically approaches unity in any gapped phase with finite ground-state degeneracy, with finite-size corrections bounded by $\mathscr{O}(1/L)$. Consequently, a non-unity value in the thermodynamic limit provides a sufficient criterion for identifying gapless fermion chains. We confirm this criterion using the $s$-wave Bardeen-Cooper-Schrieffer (BCS) Hamiltonian and determinant quantum Monte Carlo (DQMC) simulations of interacting Hubbard models. We further extend the twisting-operator approach to SU($N$)-symmetric fermionic systems, where the gapped ground-state sector must be SU($N$)-singlet and $\langle \hat{\mathcal{U}}^M\rangle=1+\mathscr{O}(1/L)$ by a fermionic twisting operator $\hat{\mathcal{U}}$ with a suitably chosen integer $M$.

Ultralight Majorons are well-motivated dark-matter candidates that can couple to electron spins, generating an oscillating pseudo-magnetic field. We propose a hybrid magnon-qubit haloscope that exploits this interaction to search for Majoron dark matter. In our scheme, the Majoron field resonantly drives the Kittel mode of a ferrimagnetic yttrium iron garnet (YIG) sphere, producing a collective magnon response enhanced by the large spin ensemble. The resulting magnon population is transduced to a superconducting transmon qubit through a cavity-mediated dispersive interaction and detected using quantum-nondemolition Ramsey interferometry. Using experimentally demonstrated parameters for magnon-cavity-qubit systems, we derive the Majoron-induced signal, evaluate the projected sensitivity, and analyze the corresponding mass-scan strategy enabled by magnetic-field tuning, benchmarking the projected reach against existing laboratory and astrophysical constraints on the axion/Majoron-electron coupling. Our results establish hybrid magnon-qubit architectures as a promising quantum-sensing platform for searches for Majoron dark matter and, more generally, ultralight bosonic fields coupled to electronic spins.

We construct an analytical thick-brane solution in linear teleparallel Gauss-Bonnet gravity using a first-order formalism generated by a sine-Gordon superpotential. The resulting asymptotically $\mathrm{AdS}_5$ configurations exhibit brane splitting controlled by the dimensionless parameter $q=4\alpha k^2$. An analytical splitting condition is derived and combined with tensor-stability requirements to identify the physically viable parameter region. We show that the tensor spectrum is free of tachyonic instabilities and supports a normalizable graviton zero mode. The massive sector exhibits odd-parity gravitational resonances whose quasi-localization is significantly enhanced near the stability boundary. Our results establish a direct link between brane splitting, tensor stability, and gravitational resonances in teleparallel Gauss-Bonnet braneworlds.

We formulate an obstruction and residual-completion theory for Newman-Janis-type deformations of black hole seeds, where Newman-Janis-type includes both the original complex-coordinate Newman-Janis algorithm and modified prescriptions such as non-complexification variants. The Newman-Janis algorithm is treated as an off-shell map from a static seed to a stationary-axisymmetric trial geometry, rather than as a solution-generating theorem. Its failure is encoded in a Newman-Janis obstruction tensor, defined as the residual obtained after substituting the trial configuration into the intended field equations. We decompose this residual into dynamical, geometrical/coordinate-admissibility, and source-preservation channels, separating field-equation failure from circularity, Boyer-Lindquist integrability, stress-tensor type, equation-of-state preservation, and matter-model realizability. When the obstruction is nonzero, residual completion asks whether a minimal correction of the metric and matter fields can cancel it. At leading nonzero order in the rotation parameter, this becomes a linear solvability problem: the obstruction must lie in the image of a gauge-fixed completion operator subject to boundary and source-sector constraints, while the cokernel condition gives a no-go criterion in the chosen ansatz class. We illustrate the framework with a Schwarzschild example in vacuum GR. Using an ONJA-type complexification different from the Kerr-generating one, we obtain a non-Kerr rotating trial metric and compute its obstruction. The example gives $n_\star=2$ and $\ell_\star=0$, with an additional quadrupolar component at the same order, and shows how the leading residual is removed by the minimal even-parity correction restoring the Kerr complexification. The framework replaces the search for the correct complexification rule with computable criteria for success, completion, or obstruction.

Deviations from vacuum general relativity (such as modified theories or the presence of an environment) produce small shifts in black hole quasinormal mode (QNM) spectra. These effects are becoming increasingly relevant for gravitational wave astronomy as observations of ringdown spectra become more precise. To leading order in deviations from vacuum general relativity, frequency shifts can be calculated using eigenvalue perturbation theory. However, for Kerr, there is no systematic framework to compute higher order corrections. The major obstacle is that QNMs do not form a complete basis due to the non-self-adjointness of the system. Nevertheless, it was recently shown that QNMs are orthogonal with respect to an appropriate bilinear form. In this work, we use the bilinear form to systematically lift Schrödinger perturbation theory to the black hole setting. We obtain a formula for quasinormal frequency shifts to any order, in terms of lower order mode shifts. We also provide a spectral decomposition of the first-order mode shift, which involves projections onto unperturbed QNMs along with continuous-spectrum contributions—making incompleteness explicit. We illustrate the framework on slowly-spinning Kerr and Pöschl-Teller examples, where we find that the QNM sum itself diverges.

A real scalar field nonminimally coupled to the curvature of an astrophysical object can develop an effective potential that supports, alongside stable oscillatory solutions, a set of tachyonic modes with purely imaginary frequencies. Focusing on constant-density Newtonian stars, we show that the tachyonic sector behaves as a collection of decoupled inverted harmonic oscillators, whose quantization is naturally addressed within the rigged Hilbert space formalism. At the quantum level, this sector is described by resonant states, with mean lifetimes determined by the associated imaginary frequencies. To probe the physical implications of this framework, we compute the transition probability of an Unruh-DeWitt detector in a circular orbit. In the presence of tachyonic modes, the detector response acquires an additional finite Lorentzian profile that modifies the standard circular Unruh-like background.

The recently observed signatures of superconductivity proximate to a fractional quantum anomalous Hall (FQAH) state in a twisted MoTe$_2$ bilayer has revitalized interest in quantum phases of matter induced by anyon dynamics. Here we show how a panoply of anyon-driven phases associated with doping the lattice ${\nu=2/3}$ FQAH state can be realized as competing instabilities of a Fermi surface of charge-$e/3$ “quarks” coupled to a $\mathrm{SU}(3)_{-1}$ Chern-Simons gauge field, which is dual to the more conventional $\mathrm{U}(1)_3$ Chern-Simons-Ginzburg-Landau theory of quasiholes. For example, a range of electronic superconductors emerge from color superconductivity, under which the Fermi surface experiences a pairing instability mediated by gauge fluctuations. These include SC$\star$ phases – where superconductivity coexists with topological order – as well as topological superconductors displaying half-integer chiral central charges when the quarks are weakly paired. One example is a $p+ip$ “color-valley-locked” superconductor, a topological analogue of the color superconductor familiar in quantum chromodynamics. On the other hand, both superconducting and non-Fermi liquid phases can emerge when the quarks form an itinerant ferromagnet, polarizing the Fermi surface to a particular combination of colors. Finally, our framework naturally accommodates the possibility of anyonic bound state formation, allowing access to phases induced by doping anyons of charge $2e/3$ as opposed to $e/3$ within the same model. Our work unifies many earlier proposed anyonic phases as instabilities of a single parent quark metal phase, distilling their emergence into a competition between superconductivity and itinerant color ferromagnetism.

We analyze confinement and screening in single-flavor quantum electrodynamics (QED$_2$) on two-dimensional anti-de Sitter space (AdS$_2$), with and without a Schwarzschild black hole, both in the continuum and on the lattice. The theory is formulated in two frames adapted to distinct choices of a preferred time coordinate: the Schwarzschild frame, associated with the Boulware vacuum, and the global AdS$_2$ frame, associated with the $\mathrm{SL}(2,\mathbb{R})$-invariant vacuum. In the massless limit, the static potential between an external charge-anticharge pair is obtained in closed form by bosonization, at both zero and finite temperature. After subtraction of the position-dependent probe self-energies, which, unlike in flat space, are not constant, the potential remains finite as the geodesic separation is taken to infinity, establishing that the theory is screened. This is consistent with the explicit breaking of the $\mathrm{U}(1)$ electric one-form symmetry by the dynamical fermions, and resolves a confining/screening ambiguity in earlier treatments that identify the static potential with the unsubtracted ground-state energy. To validate the continuum analysis, we propose a covariant discretization scheme for placing fermions in curved spacetime on the lattice while ensuring that the continuum properties of the spin and gauge connections are restored in the continuum limit. This construction resolves ambiguities in the existing literature on lattice fermions in curved backgrounds and provides the foundation for our tensor-network simulations. Using a matrix product state ansatz, we confirm our analytical predictions for the phase diagram in AdS$_2$. We perform extensive numerical simulations of the static potential and the electric flux-tube profile for varying fermion masses, which we match to the continuum prediction.

We study conformal Quantum Electrodynamics (QED) coupled to either $N_f$ massless fermions or $N_s$ conformally coupled scalars in Euclidean Anti-de Sitter (AdS$_d$) space for $d < 4$. Using the $\epsilon$-expansion around $d=4$, we investigate the associated Boundary Conformal Field Theories (BCFTs) defined by imposing either Dirichlet or Neumann boundary conditions on the gauge field. We compute the regularized AdS free energy at the interacting fixed point up to next-to-leading order and extract some of the boundary conformal data at one loop, including the anomalous dimensions of the lightest singlet scalar operators. For Dirichlet boundary conditions, extrapolation of our $\epsilon$-expansion results indicate that one of these scalar operators, which is irrelevant near $d=4$, reaches marginality within the range $3 < d < 4$. This suggests that the Dirichlet boundary condition may not define a stable BCFT in $d=3$.

We introduce and solve a new family of two-dimensional string theories obtained by coupling Liouville CFT to the generalized Runkel-Watts CFT. By taking an appropriate limit of the complex Liouville string, we derive an all-genus formula for its string amplitudes, and formulate a duality with a matrix integral. We explain that it can be interpreted as 2d SU(2) Yang-Mills theory coupled to gravity. We show that it also directly relates to other minimal string constructions such as the A-series minimal string.

Five-dimensional superconformal field theories ($5d$ SCFTs) can be encoded by Generalized Toric Polygons (GTPs), where external legs of the dual $(p,q)$ five-brane web correspond to $T$-cones. Hanany-Witten transitions act on these geometries by flipping $T$-cones about their apex, thereby naturally endowing the choice of origin in the polygon with physical significance. It was recently conjectured that a suitably graded Hilbert series equals the Ehrhart series of the dual polytope, which, in turn, is an invariant under such mutations. In this paper, we introduce a prescription for assigning scaling dimensions to fields in the toric gauge theory associated with the underlying toric diagram and show that the resulting Hilbert series of the coherent component of the moduli space matches the geometric Hilbert series given by the Ehrhart series of the dual polytope once an origin is specified. We validate our construction through several non-trivial examples, including cases with multiple admissible choices of origin leading to distinct GTPs and brane-web realizations. Our results provide evidence that ordinary brane tilings retain non-trivial information about generalized toric polygons and suggest the existence of a deeper combinatorial structure underlying GTPs.

Using the formalism of the flavor spin theory, we re-derive the TM1 lepton flavor mixing factor decomposition in a novel way, using a previously unreported near identity involving the elements of the first row of U_PMNS. The resulting mixing matrix is a direct consequence of the conformal symmetry of the massless SM before the EW phase transition. In addition to the previously reported results, we derive a relation between the CP violating phase and the three mixing angles. Application of the relation to the experimental data data suggests the TM1 decomposition should use (19/12)Pi as the value for the CP violating phase. With this assumption all four parameters of TM1 may be expressed in radicals, which might help in the separation of the classical values of the mixing parameters from their quantum corrections in the framework of the flavor spin theories. This in turn could help in clarification of the mass generation mechanism.

We construct an asymptotically flat T-fold representative of a four-dimensional dyonic black-hole charge orbit in doubled type-IIB theory. Starting from the F1-P-NS5-KKM toroidal seed, an integral parabolic T-duality monodromy is imposed on an active doubled three-torus. The non-geometric data enter only through this global patching: the Reissner-Nordström-type term is sourced by conserved four-dimensional electric and magnetic field strengths in the doubled Kaluza-Klein/winding local system, not by an internal algebraic \(Q\)-flux alone. Exact duality preserves the local equations, the BPS index, and the \(O(6,6)\)-invariant of the NS-NS/\(N=4\) charge sublattice governing the entropy. The minimal Einstein-Maxwell-dilaton slice contains a running-scalar branch and an equal-charge Reissner-Nordström limit; the extremal near-horizon region is locally \(\mathrm{AdS}_2\times S^2\), with the compact factor globally T-duality patched.

Gravitational wave astronomy provides a powerful avenue for probing exotic compact stars. Recent analyses of GW170817 have reported possible post-merger gravitational wave echoes with a significance of $4.2\sigma$ and a dominant frequency near $72,\text{Hz}$. Such echoes may arise from ultracompact remnants possessing photon spheres that partially trap gravitational perturbations. In general relativity, photon-sphere formation requires the stellar compactness to lie between one-third and four-ninths, a condition difficult to achieve with realistic equations of state. Here, we investigate this possibility in quadratic curvature gravity with non-minimal matter coupling, considering strange stars described by the MIT bag model equation of state. By solving the modified Tolman-Oppenheimer-Volkoff equations, we obtain mass-radius relations and identify configurations capable of supporting photon spheres and gravitational wave echoes. The modified Buchdahl limit permits more compact stellar solutions, while photon-sphere constraints restrict the viable parameter space. We find that increasing the bag constant reduces the maximum mass and echo time, shifting the echo frequency toward the kHz regime. The echo constraints impose more stringent maximum mass-radius limits than hydrostatic equilibrium, suggesting revised maximum mass bounds for strange stars. We further compute the critical impact parameter and eikonal quasi-normal modes, demonstrating how modified gravity parameters systematically alter the photon-sphere radius and associated observational signatures. These results establish post-merger strange stars as potential GW echo sources and highlight echoes, optical shadows, and QNMs as complementary probes of modified gravity for next-generation detectors such as the Einstein Telescope and Cosmic Explorer.

We apply the free-field construction of the heterotic string compactified on Berglund–Hübsch Calabi–Yau orbifolds by computing the full spectrum of massless $E_6$ singlets. The contribution of the descendant vertices is obtained by combining the exact content of the irreducible $N=2$ minimal model representations, encoded in the ranks of the Shapovalov matrices, with the twisted sector structure of the orbifold. The method reproduces the known spectrum of the quintic orbifold with Hodge numbers $(17,21)$, namely $17$ generations, $21$ antigenerations and $234$ singlets. For the quintic itself we obtain $330$ singlets. We show that this number, rather than the frequently quoted value $326$, obtained from the geometric description, is the correct one at the Gepner point, in agreement with the Landau–Ginzburg computation of Kachru and Witten. We also provide an explicit construction of the general vertices. We then compute the new spectra of the two remaining quintic orbifolds, $Z_5[0,1,2,3,4]$ with $(21,1,210)$ and $Z_5[0,0,0,1,4]$ with $(49,5,258)$, where the exceptional Hodge number $h^{2,1}=49$ arises from the twisted sectors. All four examples satisfy exact mirror-symmetry checks.

We investigate the statistical properties of random quadrangular surfaces generated by different randomization procedures: the Gruzberg-Klümper-Nuding-Sedrakyan (GKNS) construction, and two newly introduced generalizations of dynamical triangulations (DT), dynamical (DQ) and general quadrangulations (GQ). We formulate these surfaces within a unified graph-theoretic framework and establish the relationships between the elementary operations defining the different ensembles. For GKNS surfaces, we demonstrate that the construction is equivalent to two mutually constrained percolation processes and determine the associated critical point and critical exponents, revealing deviations from ordinary percolation. For DQ and GQ, we analyze the underlying Markov chains and determine the scaling of mixing and relaxation times. We further analyze all three ensembles through their degree distributions, degree correlations, distance statistics, and Hausdorff dimensions. While DQ exhibits exponentially decaying degree distributions and geometric properties similar to DT, GKNS and GQ display broad, scale-free degree distributions. Moreover, GKNS surfaces possess an asymptotic Hausdorff dimension $\Delta_H\approx 2$, whereas DQ and GQ approach $\Delta_H\approx 4$, similarly to DT. This indicates that DQ is compatible with the universal behavior of DT, while GKNS and GQ define distinct classes of random geometry, implying a different underlying measure in the space of random surfaces and a possible geometric framework for a new class of noncritical string theories.

We investigate a class of local quantum quenches in which the conformal boundary condition of a (1+1)-dimensional conformal field theory is abruptly changed. We derive a remarkably simple and universal expression for the time evolution of one-point functions on the half-line. This result provides a direct description of the propagation of the disturbance generated by the quench and, in turn, allows us to determine the dynamics of bipartite entanglement for subsystems adjacent to the boundary. We show that, once the subsystem becomes fully causally connected to the quench event, the entanglement entropy undergoes a sharp finite jump whose magnitude is universally given by the logarithm of the ratio of the boundary g-factors associated with the initial and final boundary conditions. We benchmark these analytical predictions against Matrix Product State simulations of the critical Ising spin chain, finding excellent agreement. The numerical analysis further allows us to investigate the time evolution of the spin-flip entanglement asymmetry, revealing how the symmetry-breaking perturbation emitted from the boundary propagates through the system. Our results uncover universal dynamical signatures of boundary quenches and establish a direct connection between nonequilibrium entanglement dynamics and boundary critical phenomena.

We construct a nuclear-matter equation of state (EOS) from holographic QCD in the Witten-Sakai-Sugimoto (WSS) model, going beyond the homogeneous ansatz by building dense baryonic matter more directly from the solitonic description of holographic baryons. Employing the two-baryon interaction potential obtained from the linearized soliton tails sourced in the curved background by point-like (core) instantons, we assemble an infinite face-centered cubic (FCC) crystal with nearest neighbors in the most attractive channel as an approximation to the quantum liquid of baryons and compute the energy density $\mathcal{E}(n_B)$, the chemical potential $\mu_B$, and the pressure $P$. We calibrate the symmetric-matter EOS by fixing the 't Hooft coupling $\lambda$ and the WSS scale $M_{\rm KK}$ to saturation-density and onset-chemical-potential properties, and by including a quark-mass term to reproduce the physical pion mass $m_\pi=135\,\mathrm{MeV}$. This fit turns out to remain reasonably close to the parameters required by the vacuum meson sector, while their modification is consistent with Brown-Rho scaling in a dense medium, and the incompressibility at saturation is of the correct order of magnitude, both in clear contrast to the homogeneous approximation. We then extend to beta-equilibrated matter, using phenomenological input for the symmetry energy, and obtain hybrid EOS and neutron-star observables that are compatible with the NICER constraints.

In recent years, a variety of three-dimensional (3d) $\mathcal{N}=2$ Chern–Simons (CS) matter theories have been constructed that flow to 3d $\mathcal{N}=4$ superconformal field theories (SCFTs) obtained from $R$-twisted reductions of four-dimensional (4d) $\mathcal{N}=2$ SCFTs. In all previously studied examples, the resulting 3d $\mathcal{N}=4$ SCFTs have trivial Coulomb branches. In this paper, we construct a 3d $\mathcal{N}=2$ CS matter theory that flows to the $R$-twisted reduction of the $(A_2,D_4)$ Argyres–Douglas theory. This gives the first example in this class whose infrared 3d $\mathcal{N}=4$ SCFT has a non-trivial Coulomb branch, which we argue is given by the orbifold $\mathbb{C}^2/\mathbb{Z}_2$, while its Higgs branch is trivial. We further identify the 4d $U(1)$ R-charge as a mixing of a 3d R-charge with an emergent 3d Coulomb branch flavor charge that has no 4d origin.

We introduce a microscopic framework that gives the first rigorous derivation of the Schwinger–Dyson thermodynamics of the Sachdev–Ye–Kitaev model. For fixed, even interaction order $q\geq 4$, we prove that the annealed and quenched normalized pressures converge to the Schwinger–Dyson pressure $p_{{\rm SD},q}(\beta)$, at any fixed inverse temperature $\beta>0$. The proof is derived from the finite-$N$ Gibbs state, and it contains three new ingredients: a single-site cavity expansion that keeps the bulk Gibbs state intact, a finite-dimensional locality estimate yielding label-uniform conditional factorization of the Euclidean cavity fields, and an exact Majorana-bath representation of the leading diagrams. We further determine the asymptotic location of the largest eigenvalue, which answers a question posed by Feng–Tian–Wei. Consequently, the sample free-energy density converges almost surely to the zero-temperature value along every sequence $\beta\equiv \beta_N\to\infty$.

Exotic compact objects (ECOs) may produce late-time gravitational-wave (GW) echoes, but sufficiently compact ECOs undergoing realistic accretion may eventually form an event horizon. We investigate the evolution of quasinormal modes and GW echoes during this transition. Modeling the exterior spacetime with the ingoing Vaidya solution, we numerically evolve scalar perturbations on the resulting dynamical background. We show that the echo signal is progressively compressed and suppressed during accretion and disappears once the growing event horizon engulfs the reflecting surface, after which the waveform smoothly approaches the standard black hole ringdown. Our results identify the disappearance of GW echoes as a characteristic signature of horizon formation and provide a framework for studying dynamical compact objects with future GW observations.

We study higher-rank generalized Killing tensors with mixed symmetries, providing a couple of examples and applications. It is shown that such objects naturally exist in higher-dimensional rotating black hole spacetimes, where they arise as partially contracted "squares" of Killing-Yano tensors and display interesting algebraic and differential properties. Motivated by conformal Killing tensors, a generalization of these objects that gives rise to parallel-transported tensors along null geodesics is proposed and shown to exist in higher-dimensional rotating black hole spacetimes.

The frozen star is a model for the interior of an astrophysical black hole that is externally indistinguishable from the singular geometry of a Schwarzschild black hole, even though it contains no singularities nor trapped surfaces. The frozen star corresponds to a macroscopic “BIon”, a solution of a certain type of Born-Infeld Lagrangian coupled to Einstein gravity, which consists of rigid flux tubes sourced by an electric charge localized at its center and a uniform distribution of opposite charge along its outer surface. This configuration is a solution of the effective action that describes the end point of tachyon condensation in string. The rigidity of the flux tubes implies that the star is ultrastable under linear perturbations of the geometry and matter. The star can be effectively deformed, or “defrosted”, allowing internal pulsations, as expected from regular, horizonless astrophysical black holes. To describe the defrosted star, we need to include a perturbative amount of magnetic-monopole charge and tachyon kinetic energy. This recasts the star as a macroscopic “DIon”, whose flux tubes can stretch and contract, having both electric and magnetic charges localized at its center and distributed uniformly along its outer surface. Previously, the non-radial oscillations of the defrosted star were analyzed to leading order in a perturbative “defrosting” parameter $\gamma$, by describing the energy-momentum tensor as that of a fluid. Here, we derive the same spectrum in a much simpler way, using the Born-Infeld Lagrangian. Thus, we verify that the sound velocities scale as $\gamma$ and the parametrically long lifetimes scale as $1/\gamma^2$. Because the perturbation equations are derived from a Lagrangian, their consistency is guaranteed for arbitrary deviations away from spherical symmetry, facilitating numerical studies on frozen stars away from equilibrium.

We investigate the transformation of Killing-Yano (KY) $p$-forms under Abelian T-duality in the presence of a non-trivial three-form torsion. Using a torsionful, metric-compatible connection and the Buscher rules of T-duality, we derive compact, coordinate-free transformation laws applicable to KY forms of arbitrary degree under explicit matching assumptions. In particular, we show that a Killing 1-form is preserved by the direct duality map whenever its transverse components are independent of the isometry direction, with the dual circle component determined by a scalar correction equation. The framework is then applied to several examples, including the Hopf T-dual of $S^3$, Schwarzschild spacetime, and the Nappi-Witten plane wave with exact NS-NS torsion, where we analyze the transformed Killing-Yano forms explicitly. Finally, we give a generalized-geometric and double-field-theoretic interpretation of emergent Killing 1-forms in the T-dual geometry, showing how they arise from generalized Killing data in the original duality frame.

Compact heavy quarkonium couples through the multipole interaction to scalar and spin-two gluonic operators. At leading chromoelectric order the corresponding matching coefficients satisfy $C_2^\Phi=-C_S^\Phi$; an independent chromomagnetic polarizability lifts this relation within the general CP-even, spin-independent, local two-gluon interaction at dimension four and zero derivative order. We construct an RG-consistent realization in a fixed $MS$ convention. The QCD trace identity converts the gluon-only scalar matching condition into an invariant basis and fixes the correlated quark-mass coefficient required when the interaction is re-expressed in the scale-dependent basis away from the matching scale, whereas leading-logarithmic singlet evolution induces a quark spin-two coefficient. In threshold-aligned symmetric kinematics, the canonical-spin non-flip projection contains $A_i(t)$ and the combination $3B_i(t)-D_i(t)$. An explicit Breit-frame calculation relates this projection to an off-diagonal helicity representation for nonzero spacelike $t$; the off-diagonal form is kinematic rather than an additional dynamical spin flip. Linearity of the scalar and spin-two evolution factorizes the chromomagnetic dependence of their ratio as $R_{2/0}^{\Phi}(t;\rho_\Phi)=[(1+\rho_\Phi)/(1-\rho_\Phi)]R_{2/0}^{\Phi}(t;0)$ within the gluon-only dimension-four matching setup. The result separates state-dependent quarkonium matching from scalar and gravitational nucleon structure and states explicitly the assumptions under which this factorization holds.