Papers

Static black holes in conformal Weyl gravity differ from their Einstein counterparts in a simple but important way: the Mannheim–Kazanas geometry is encoded in a Bach-flat lapse function whose radial dependence is richer than that of Schwarzschild–de Sitter. We study the de Sitter branch of this solution in the Schwarzschild gauge, keeping the characteristic linear term together with the quadratic de Sitter term. In the branch continuously connected to the positive-mass Schwarzschild–de Sitter spacetime, a regular static region between a black-hole horizon and a cosmological horizon exists precisely when \[ -\frac{1}{3}<\beta\gamma<\frac{2}{3}, \qquad 0<\kappa<\frac{1+3\beta\gamma}{27\beta^{2}}. \] In this window the singularity at the origin is hidden, the two positive horizons obey $0<r_b<3\beta<r_c$, and the limiting endpoint is the Nariai geometry. The thermodynamic interpretation is subtler than the root structure: the two horizons generally have different temperatures, and the static patch has no asymptotic region that would select a unique normalization of time. We therefore compare the Killing, Bousso–Hawking normalized, Tolman local, and effective two-horizon temperature conventions, and we compute the corresponding Wald entropy for the pure Weyl-squared action. The result is a local horizon thermodynamic description that keeps the geometric facts separate from the ensemble-dependent choices needed for any global first law.

The Snyder–de Sitter algebra provides a Lorentz-covariant deformation of phase-space geometry characterized by a curvature parameter $\alpha$ and a noncommutativity parameter $\beta$. We construct an explicit canonical (Darboux) representation of this algebra that is regular in both parameters. Starting from the symplectic structure associated with the Snyder–de Sitter Poisson brackets, we derive the canonical transformation between the physical phase-space variables and Darboux coordinates and obtain its inverse in closed form to all orders in $\alpha$ and $\beta$. The resulting representation has well-defined flat ($\alpha\to0$) and commutative ($\beta\to0$) limits, reducing respectively to the Snyder and de Sitter phase-space algebras, while the simultaneous limit $(\alpha,\beta)\to(0,0)$ yields the standard canonical phase-space coordinates. We then apply this representation to the construction of Poisson gauge transformations on Snyder–de Sitter phase space. In particular, we derive the corresponding gauge transformation matrix and Poisson field strength, both of which are regular in $\alpha$ and $\beta$. Our construction provides a convenient framework for investigating gauge theories and other physical systems formulated on Snyder–de Sitter phase space.

We construct four bounded Hermitian operators, each one a finite polynomial in the unitary Weyl operators, for the Bell-CHSH inequality in a free massive scalar field in $1+1$ dimensions. The operators are localized in complementary wedges. Odd Weyl harmonics provide two exactly anticommuting axis observables in each wedge, while normalizable packets with compact support in the spectrum of the boost generator give exact modular inner products at nonvanishing bandwidth. The resulting Bell-CHSH correlator is a finite double sum. An operator with six Weyl terms per axis already gives $2.14885$. Using normalized Fejér approximants of $\operatorname{sgn}(\cos(x))$, we show that the supremum over the finite-polynomial family equals $2\sqrt{2}$, although no finite member attains it; a degree-$511$ example gives $2.80027$. We also point out that, in a centered quasifree state, a Bell-CHSH test whose four final settings are bounded functions of individual quadratures admits one common Gaussian representation and therefore stays below $2$. The finite-Weyl construction avoids this restriction because Bob's final settings mix two noncommuting axis observables.

We construct representation-independent families of solutions of the non-braided scalene Yang–Baxter equation from quadratic noncommutative algebras. Beginning with two anticommuting generators, we obtain a continuous deformation in terms of quantum-plane algebras and extend the construction to an arbitrary number of generators. In the latter case the scalene Yang–Baxter relation fixes the multiparameter exchange matrix to an exact multiplicative form, thereby selecting a distinguished subclass of multiparameter quantum affine spaces. We construct finite-dimensional realizations using singular matrices and finite Heisenberg–Weyl operators, as well as infinite-dimensional realizations in terms of bilateral weighted shifts and multiplicative-shift operators. The explicit realizations are generically purely scalene: although the ordered triple satisfies the scalene Yang–Baxter equation, its individual constituent operators do not satisfy the ordinary non-braided Yang–Baxter equation. These results provide a representation-independent algebraic framework for constructing Yang–Baxter-irreducible scalene triples and a starting point for investigating their possible applications to quantum integrability.

We study phase transitions out of a (2+1)d topological phase driven by the proliferation of anyons in a braided fusion subcategory. We describe a general theoretical framework for such transitions, in which the topological quantum field theory (TQFT) is coupled to dynamical matter associated with anyons in the subcategory. We interpret this construction using symmetry topological field theory (SymTFT), where the dynamics is localized on the symmetry boundary of the (3+1)d slab. We analyze several examples, and present explicit Chern-Simons-Higgs (CSH) field theories realizing the proliferation transitions. We also examine proliferation transitions that implement gauging of non-invertible one-form symmetry in the parent TQFT. This includes a general construction for ${\rm Rep}(G)$ one-form symmetry for a finite group $G$, and a CSH realization of the non-invertible one-form gauging ${\rm SU}(2)_{10}\rightarrow {\rm Spin}(5)_1$. We discuss which anyons proliferate at these transitions.

Minimal surfaces govern the classical limit of several important observables in string theory. Two basic examples are the Gross–Manes saddle for high-energy string scattering in flat space and the Alday–Maldacena surface for gluon scattering at strong coupling in ${\cal N}=4$ SYM. In this paper we study a family of null polygonal minimal surfaces in AdS interpolating between these two regimes by moving the cusps from a small region deep in the bulk to the AdS boundary. We do this both numerically and – in interesting simplifying limits – analytically. In particular, we derive the leading AdS-radius correction around flat space and show that the resulting classical amplitude agrees with the recent prediction of Alday, Armanini, Häring, and Zhiboedov, supporting an underlying worldsheet description of their bootstrap construction.

There are four known ${N}{=}1$ supersymmetric Virasoro minimal string theories, naturally coming in two pairs and labeled as 0A$^\pm$ and 0B$^\pm$. We observe here that all four are naturally described in terms of solutions of an ordinary differential equation that describes certain random matrix models with positive spectra. Two new additional 0A$^-$ theories, which are unorientable, are naturally described by the framework. The formulation allows for simple computation of all perturbative amplitudes, and provides complete non-perturbative information as well. Our approach makes it clear why type 0A$^-$ can be deformed to include a gas of Ramond vertex insertions, which we fully describe, while type 0A$^+$ cannot. While it is known that the $c\rightarrow\infty$ limit reduces the 0A$^-$ and 0B$^-$ models to the familiar 0A and 0B JT supergravities of Stanford and Witten, the same limit for the plus pair reduces to non-perturbative completions of ordinary JT gravity, one of which is known. Large families of ${N}{=}2$ and ${N}{=}4$ supersymmetric analogues of the Virasoro minimal strings are also proposed and explored in detail, using the same approach.

We introduce the notion of a total inner product on an $A_\infty$-algebra, and a cyclic Chern-Simons form associated to a topologically nilpotent element. The total inner product applied to the cyclic Chern-Simons form gives a superpotential function that is gauge invariant on solutions of the Maurer-Cartan equation known as bounding cochains. The derivative of the superpotential is computed. The definition of total inner product replaces strict symmetries that appear in previous notions of homotopy inner products with symmetries up to an infinite family of coherent homotopies. We show how to recover previous notions of homotopy inner products as special cases of total inner products. Total inner products are designed to facilitate the definition of descendent open Gromov-Witten invariants. The definitions of the total inner product and the cyclic Chern-Simons form use the total complex of cyclic codifferential forms, which gives a chain model for cyclic homology. We give explicit formulas for homotopy equivalences with other known models. We discuss also the notion of an $\infty$-trace, which arises from Connes' cyclic complex, and the associated $\infty$-modulus, which gives another gauge-invariant function on bounding cochains. In open Gromov-Witten theory, the $\infty$-modulus is used to normalize the bounding cochains to which the superpotential is applied. We develop our definitions for general curved Banach $A_\infty$-algebras, and give both unital and non-unital versions of the main results. In the unital setting, we work with weak bounding cochains, solutions of an inhomogeneous Maurer-Cartan equation involving the unit. Weak bounding cochains arise in the open Gromov-Witten theory of Lagrangian submanifolds with non-vanishing Maslov class. The derivative of the superpotential at a weak bounding cochain is related to the derivative of the $\infty$-modulus.

In this work, we investigate the worldline deviation of spinning test particles in a weak gravitational wave (GW) spacetime. Within the pole-dipole approximation and the Tulczyjew spin supplementary condition, we consider the modified deviation equation, which contains the standard geodesic deviation term and an additional contribution generated by the Mathisson-Papapetrou-Dixon (MPD) force. We demonstrate how the deviation equation can be solved under viable approximations to yield a new expression for the change in the deviation vector in terms of the perturbation $h_{ij}$, its time derivative, the spin vector components and the longitudinal and transverse components of the deviation. The spin-curvature coupling is shown to play a crucial role in controlling the change in deviation. We then use this result to investigate the changes in the form and expressions of the net GW signal as well as our understanding of GW memory, in the presence of spin. We conclude with our attempts on the measurability of this spin-induced effect vis-a-vis present GW observations.

We use conformal perturbation theory to compute one-loop threshold corrections to the Kähler potential of the heterotic string. For this we consider the theory compactified at the Gepner point of the quintic, that is at a highly stringy point of its moduli space. To obtain the corrections, we compute how the weights of the lightest states of the worldsheet theory shift at second order in conformal perturbation theory. This approach can be used to obtain the one-loop correction to all orders in $\alpha'$.

We study the one-point probability distribution function (PDF) for matter densities averaged with an arbitrary spherically symmetric window function. The PDF is analytically modeled within the path integral framework, enabling a non-perturbative description of large-scale structure. It contains a leading order contribution controlled by the spherically symmetric gravitational collapse dynamics, as well as an order-one factor arising from aspherical fluctuations. We develop a numerical pipeline to compute the leading spherical-collapse part of the PDF and apply it to a family of window functions interpolating between the TopHat and Gaussian filters in coordinate space, as well as to a window function with non-monotonic radial dependence. We find that the PDF weakly depends on the choice of the filter, provided the width of the filter is normalized to yield a fixed linear averaged density variance. For each filter and each value of the averaged density, our pipeline gives the most probable density profile. We find that these profiles vastly differ for different filters in the case of overdensities, but closely follow a universal curve at underdensities. We obtain a perturbative expression for the aspherical part of the PDF valid at small density contrasts. We find from it that all PDFs are equally sensitive to the effective field theory (EFT) corrections accounting for short-scale clustering, regardless of how smooth the filter's boundary is. We test our PDF model against the results of high-resolution N-body simulations. The agreement is excellent for filters with widths larger than 10 Mpc/h. Small discrepancies at a few percent level arise for narrower filters and are interpreted as higher-order perturbative corrections.

Superspace extends spacetime by anticommuting Grassmann coordinates, whose indices may transform under spin and flavour groups. Decomposing Grassmann monomials into independent invariant structures is a central step in constructing superfield expansions, but becomes increasingly difficult in extended superspace. We present a general representation-theoretic procedure for decomposing the space $\Lambda^n(\mathbb{C}^{d_S}\otimes \mathbb{C}^{d_F})$, where $d_S$ and $d_F$ are the dimensions of the spin and flavour representations. The branching multiplicities for $\mathrm{GL}(m)\downarrow{\mathrm{Sp}(m)}$ and $\mathrm{GL}(m)\downarrow{\mathrm{SO}(m)}$ are computed by exact Weyl-character comparison at deterministic rational sample points, avoiding Littlewood-Richardson modification rules. We establish completeness of the character ansatz and analyse the computational complexity, showing that it is polynomial in the number of partitions of $n$ and in the group rank, without dependence on Littlewood-Richardson combinatorics. We validate the resulting decompositions via dimension checks. We provide an accompanying standalone Julia script which implements this algorithm for groups of arbitrary rank, and produces the explicit contractions with invariant tensors.

We present "Alakazam", a Julia package for performing symbolic manipulations of tensor expressions arising in the study of field theories and quantum mechanics. This will serve as a powerful tool for studying spacetime and supersymmetric structures, including support for calculations in superspace. The package implements many key features such as raising and lowering indices, simplification of terms with dummy indices, replacement patterns, differential and variational calculus, bosonic and fermionic grading, gamma matrix identities, and Lie brackets and commutators. We present notable speed improvements over established systems. Some possible applications include the study of descendants and invariants.

A tangle of line defects coarsens as the mean spacing $L$ between neighbouring lines grows. In a viscous medium the motion is overdamped, and the velocity-dependent one-scale (VOS) model predicts a late-time attractor $L^{2}=\mathcal{A}\,\ell_d\,t$, with $\ell_d=T/\Gamma$ the ratio of line tension to drag and $\mathcal{A}$ a dimensionless amplitude. The growth law $L\propto t^{1/2}$ holds for every value of the three model parameters—the momentum parameter $k\le1$, the sink coefficient $\tilde{c}$, and the curvature ratio $\lambda\equiv R/L$—since all three enter only through $\mathcal{A}=\kappa(\kappa+\tilde{c})$, $\kappa\equiv k/\lambda$. Thus, the exponent constrains none of them, and the amplitude is the only quantity a density history can deliver. We measure it from the disclination data of Chuang, Turok and Yurke on a nematic liquid crystal, whose companion measurement of loop collapse fixes $\ell_d$ on the same samples, canceling the 5CB material constants. Treating the unmatched per-quench $\ell_d$ as a nuisance parameter with a Gaussian prior and marginalizing it analytically, we obtain $\mathcal{A}=10.0^{+1.3}_{-1.1}$ from the three quenches in the $234~\mu$m cell; the fourth, the only one in the thinner $158~\mu$m cell, gives $\mathcal{A}=3.0^{+0.8}_{-0.6}$ and is fitted separately. Converting either into $\tilde{c}$ requires $\lambda$, which these data do not determine, so the result is a curve, $\tilde{c}(\lambda)=\mathcal{A}\lambda/k-k/\lambda$, not a number. At $\lambda=1$ with $k\le1$ they give $\tilde{c}\ge9.0$ and $\tilde{c}\ge2.0$, against $\tilde{c}=0.23$–$0.57$ from relativistic $U(1)$ simulations, values reached only at $\lambda\simeq0.33$–$0.35$ and $0.62$–$0.68$. We know of no VOS calibration for a cosmological $\mathbb{Z}_2$ network, so we cannot attribute the excess to topology, and we list what a repeat experiment must measure.

We determine the maximal torus topological entanglement entropy (TEE) at bounded torus ground-state degeneracy within simply connected untwisted Wess–Zumino–Witten theories. For a fixed modular tensor category $\mathcal C$, maximization over normalized torus ground states gives $\max_\psi\Gamma_{T^2}(\psi)=2\log{\mathcal D(\mathcal C)}$, attained in particular by the vacuum-flux state. The remaining problem is therefore to maximize total $\mathcal D$ at bounded categorical rank. For a simple WZW category $\mathcal C(\mathfrak g,k)$, write $r(\mathfrak g,k)$ and $\mathcal D(\mathfrak g,k)$ for its categorical rank and total quantum dimension, and define $F_{\WZW}(R)=\sup_{r(\mathfrak g,k)\leq R}2\log\mathcal D(\mathfrak g,k)$. We prove the sharp asymptotic law $\lim_{R\to\infty}\frac{F_{\WZW}(R)}{(\log_2R)^2} =\frac{7\zeta(3)}{4\pi^2}.$ The balanced symplectic sequence $Sp(2n)_n$ attains the coefficient. The constant arises from the odd Fourier modes of the type-$C$ root product at equal rank and level. A sharp entropy–spectral inequality, rank-level duality, and fixed-rank estimates give the global upper bound. A separate corollary extends the same leading law to semisimple WZW categories,equivalently finite Deligne products of simple factors. The unrestricted TQFT envelope remains open; the theorem is sharp within the stated WZW class and supplies a constructive lower bound for the general problem.

We show that for Abelian Chern-Simons topological orders, torus Berry matrices determine the all-genus extended TQFT. We identify the topological part of the projective Berry holonomy under metric deformations with the mapping-class-group representation of the Abelian Chern-Simons TQFT and prove that the normalized torus data reconstruct its finite quadratic module (G,q). Recent work showed that (G,q) classifies the extended theory up to symmetric monoidal natural isomorphism, and that the associated Abelian defect extension is determined by the pointed modular category C(G,q) arising from the same finite quadratic-module data. Therefore genus-one Berry data determine not only the all-genus bulk theory but also its associated defect structures without choosing a K-matrix presentation. We also prove that, for normalized character row errors $\delta$<21.96%, nearest-row decoding recovers the Abelian fusion algebra independently of the number of anyons. The result applies to Abelian fractional quantum Hall and spin-liquid phases described by even-lattice Chern-Simons theories.

Heisenberg uncertainties lead to inevitable fluctuations in the measurement outcomes for quantum-mechanical observables. For quantum fields, these uncertainties result in random spatial structures in snapshots of a field, even when the field is in its ground (vacuum) state. Such `vacuum fluctuations' are at the heart of a wide range of phenomena, from spontaneous decay processes to the Casimir force and Hawking radiation. Their existence is a key manifestation of the quantumness of the physical world, but usually it is only their consequences that are directly observed. Here, we directly observe spatial vacuum fluctuations of a bosonic quantum field. Our experiments are based on a homogeneous planar atomic Bose–Einstein condensate. The condensate comprises two coherently coupled interacting components (spin states), and the quantum field describes its spin degrees of freedom. In the regime where the interactions dominate over the coherent coupling, our system emulates a (massive relativistic) sine-Gordon field. Images of the field reveal simultaneous fluctuations on different length scales, with scale-dependent amplitudes consistent with theoretical predictions for a vacuum state. Observing such fluctuations in the sine-Gordon limit opens many possibilities for laboratory simulations of relativistic fields in regimes that are presently not theoretically tractable.

Near $(1+1)$-dimensional [$(1+1)$D] Ising criticality, a magnetic perturbation induces confinement and produces a cascade of bound-state excitations known as mesons. Here we show these mesons share a universal mass scaling after independently rescaling the model-dependent microscopic couplings. The number of stable mesons is controlled by the lightest two-meson threshold, while the lightest-meson mass follows a continuous trajectory characterized by a single scaling parameter. Using Hamiltonian truncation method, we obtain the trajectory numerically in both Ising field theory and the near-critical mixed-field Ising chain (MFIC). Under the rescaling, the trajectory and stable-meson-count crossover windows of MFIC both collapse onto the field-theory results. To further demonstrate the above universal organization of the meson spectra, we consider a class of four-periodic spin-$1/2$ Heisenberg-Ising chains under transverse fields, whose parameter space contains a family of quantum Ising critical points. The Hamiltonian family includes effective spin models for the quasi-one-dimensional antiferromagnets Ba(Sr)Co$_2$V$_2$O$_8$. Using tensor-network calculations, we obtain the corresponding lightest-meson mass trajectory for BaCo$_2$V$_2$O$_8$ and find that it also collapse onto the same universal curve given by field-theory result. Our results suggest that the universal scaling structure of quantum Ising criticality extends into the nearby confining regime, governing the organization of the meson spectrum. They thereby provide a practical criterion for interpreting excitations of quasi-1D Ising-like magnets in mixed fields beyond $E_8$ integrability.

We use lattice methods to study inflation in the scalar Gauss-Bonnet (SGB) gravity theory. We focus on the ultra-slow-roll scenario with the peak frequency falls into the PTA band. In the parameter range we consider, we find that the lattice results exceed the perturbative predictions, which differs from the case in Einstein gravity. We further find that lattice corrections become significant when the peak of the primordial curvature spectrum reaches $\sim 10^{-2}$. We calculate the energy density spectra of second-order scalar induced gravitational waves (SIGWs) using the primordial power spectra obtained from both the lattice method and the traditional perturbative method, and analyze the SGB model in light of current pulsar timing array (PTA) observations. Our results indicate that lattice corrections enhance the ability of the SGB model to dominate the PTA observations.

We investigate the Quark-Diquark Model (QDM) with the Functional Renormalization Group (FRG) in the Local Potential Approximation. In a recent work [arXiv:2510.01066 [hep-ph]], problems were reported in applying this method at low temperatures and large quark chemical potentials, which were attributed to numerical artifacts. In this work, we trace the origin of these problems to the occurrence of a negative diffusion coefficient during the FRG flow of the derivative of the effective potential, leading to strong oscillations of the latter quantity. We show that negative diffusion is a model feature and not a numerical artifact. We propose a regularization scheme which introduces a hyperdiffusion term to remove these oscillations and demonstrate its effectiveness for studies of the phase diagram of the QDM. Regularizing the negative diffusion in the FRG flow is particularly important to reliably study phenomena such as color superconductivity and inhomogeneous phases, which might emerge in the high-density, low-temperature region of the QCD phase diagram.

Global quenches at one-dimensional critical points admit a boundary conformal field theory (BCFT) description in which Euclidean strip correlators are analytically continued to real time. We formulate this construction for interacting non-Hermitian critical systems, where a right ket alone does not specify the dynamical readout and the left covector is part of the microscopic quench protocol. Independent left and right preparations flowing to the same conformal boundary define the two temporal boundaries of a strip with generally complex one-sided extrapolation parameters; linear and antilinear symmetry pairings are exploited to constrain this geometry. In the interacting Yang-Lee spin chain, statically calibrated boundary data determine the biorthogonal dynamics of the complete-character return amplitude, a primary one-point function, and a spatial correlator. The imaginary part of the linear-paired extrapolation parameter predicts the temporal center of an independently evolved antilinear-paired one-point function at the $10^{-3}$ relative level; the same preparation phase controls local phase evolution and the analytic-continuation path of boundary blocks. Further results test this formalism with a direct field-on quench, mixed left and right preparations, and a complex five-state Potts fixed point with complex primary dimensions. These results establish a BCFT framework for biorthogonal global quenches in interacting non-Hermitian critical systems, in which complex temporal-boundary data organize universal post-quench dynamics.

We study an extension of the unimodular cosmological inflation in the context of the non-minimal coupling of a generic scalar field with gravitational sector. We consider the non-minimal coupling of the scalar field and gravity as the only source of energy-momentum tensor in this setup. Without introducing new particles other than those already existing in electroweak theory, the generic scalar field's non-minimal coupling is responsible for the generation of the seeds of perturbations for structure formation and the observed Cosmic Microwave Background anisotropies in this scenario. We calculate inflation parameters in both the Jordan and Einstein frames, and then we study primordial spectral indices for slow-roll parameters in Einstein's frame at the first and second orders. The numerical results of this model are consistent with the Planck2018 and BICEP/Keck joint data sets in some subspaces of the model parameters space. By considering a sufficient amount of inflation, we estimate the strength of the non-minimal coupling parameter, $\xi$, to find appropriate new constraints on the values of this parameter. By comparing the numerical values of the inflation observables in two frames and also with observation, we comment on the issue of frames in this framework.

We study singular generalized Dirac-oscillator couplings in the near-horizon region of a nonextremal BTZ black hole. An effective covariant construction adapted to the stationary horizon congruence relates the two singular profiles to the proper acceleration and its radial gradient, whose leading near-horizon behaviors are $1/\rho$ and $1/\rho^2$. This motivates the family $\mathcal{L}_p(\rho)=\lambda_0+\beta_p/\rho^p$, with $p=1,2$. The $p=1$ system has a regular singular point and is Fuchsian, whereas $p=2$ is the first irregular case; more generally, a leading $\rho^{-p}$ interaction with $p>1$ has Poincaré rank $p-1$. For $p=1$, a constant spinor transformation reduces the matrix-Coulomb system exactly to the Whittaker equation, while elimination in the original basis gives an equivalent confluent-Heun representation with an apparent finite singularity. For $p=2$, the local branches contain the essential factors $e^{\pm\beta_2/\rho}\rho^{-1/2}$, and their coefficient expansions exhibit generic factorial late-order growth. The finite-radius response $\mathcal{Z}_p(\Omega;\rho_0)=\psi_{2,p}(\rho_0)/\psi_{1,p}(\rho_0)$ obeys an exact Riccati equation whose large-damping expansion first becomes sensitive to the radial gradient of the interaction at order $\gamma^{-3}$. Even when the two couplings are matched at $\rho_0$, this response retains information about their different pole orders. The response functions provide local spinorial data for subsequent matching to the complete BTZ exterior.

We investigate the specific heat and isentropic bulk modulus of finite-temperature pure SU(3) gauge matter within a lattice-data-driven phenomenological framework. The equation of state is formulated in terms of a temperature-dependent effective gluon mass constrained { by lattice QCD pressure data as input, allowing the pressure}, trace anomaly, gluon number density, energy per thermally active gluonic mode, and derivative-sensitive response functions to be derived in a thermodynamically consistent manner. The resulting pressure and trace anomaly reproduce the characteristic lattice behavior across the deconfinement region, while the effective gluonic degrees of freedom increase rapidly above $T_c$. The normalized specific heat $C_V/T^3$ develops a pronounced enhancement in the vicinity of $T_c$, reflecting the rapid temperature variation of the energy density across the deconfinement region. The isentropic bulk modulus $K_S/T^4$ also rises sharply across the transition region, indicating a substantial stiffening of the equation of state. At high temperatures, both response functions gradually approach values close to their massless conformal Stefan–Boltzmann reference values, with $\left(C_V/T^3\right)_{\rm SB}=32\pi^2/15\simeq 21.06$ and $\left(K_S/T^4\right)_{\rm SB}=32\pi^2/135\simeq 2.34$. These findings indicate that the specific heat and isentropic bulk modulus provide complementary constraints on the temperature evolution of nonconformal dynamics in pure SU(3) gauge matter.

De Sitter unitarity and reflection positivity are logically independent. We study their relation for a free scalar field on a fixed de Sitter background, restricting attention to the one-particle sector. Motivated by Witten's de Sitter pairing and the radial adjoint of Bousso, Maloney and Strominger, we compose the invariant Hilbert product with equatorial reflection. In the standard principal-series realization, this form vanishes identically and its Osterwalder-Schrader quotient contains no states. For the complementary series, the reflected product becomes a nonzero reflected kernel on the unit ball. A result of Neeb and Ólafsson shows that this kernel is positive semidefinite precisely when the lower weight satisfies the scalar conformal unitarity bound. The resulting Hilbert space with the reflected inner product furnishes a positive-energy representation of AdS isometries according to Neeb and Ólafsson. We identify that the range coincides with the Klebanov-Witten alternative-quantization window from physics point of view. This correspondence suggests a novel relation from the representation viewpoint between AdS and dS without the conventional analytic continuation of radius.

The post-Minkowskian expansion of general relativity expands the metric in Newton's constant G around flat space-time, but much effort currently focuses on ways to extend its range of applicability by summing the perturbative series to all orders. A regime of particular interest is a specific high-energy limit where a formula derived recently provides the momentum kick of binary scattering problem to all orders, and even suggests an approach towards strong coupling. We show that this is an asymptotic expansion. Although the series diverges we give evidence that it is Borel summable, and the full function in integral form is finite. As a by-product we determine the transcendentality properties of the coefficients in the expanded expression.

In this work, we consider the interaction of massless $N=1$ supergravity with a massive (2,3/2,3/2,1) supermultiplet, as a possible candidate for a supersymmetric extension to bigravity. A gauge invariant description for massive spin-2, spin-3/2 and spin-1 fields is used. As a result of this, ambiguities arise related to possible field redefinitions, which are fixed by using a recently proposed method based on unfolded equations, and by restricting ourselves to interactions with the minimum number of derivatives (two for bosonic and one for fermionic vertices). It appears that this completely fixes the entire construction.

In previous work arXiv:2604.00160, we found soliton solutions in a deformation of the sine-Gordon theory in AdS spacetime that, in the infinite-radius limit, reduce to single-soliton solutions in flat space. In this paper, we find another single soliton solution that has no analog in flat space.

We identify CFT counterparts of Synge's identity for finite AdS geodesics in arbitrary dimensions. Starting from exact finite bulk–boundary pairs, the Synge equation induces endpoint scale equations for a Weyl-frame scalar two-point function and for the finite entanglement entropy between disjoint balls. In the planar frame, the common-scale correlator equation is the dilatation Ward identity. In the entanglement sector, the corresponding relative-scale equation is governed by a transverse hyperbolic area and reduces in two dimensions to the previously identified entanglement RG equation.

Let $W_{\cal O}[J]$ and $W_{\cal C}[J]$ denote the connected generating functionals of an open system and its closed system counterpart, and define the environment-induced contribution $W_{\rm IF}[J]$ by the difference: $ W_{\rm IF}[J]\equiv W_{\cal O}[J]-W_{\cal C}[J].$ The corresponding Legendre transforms, $\Gamma_{\cal O}$, $\Gamma_{\cal C}$, and $\Gamma_{\rm IF}$, do not obey an analogous additive relation but satisfy a stationary composition law given by: \[ \Gamma_{\cal O}[\Phi] = \operatorname*{Stat}_{\Psi} \left\{ \Gamma_{\cal C}[\Psi] + \Gamma_{\rm IF}[\Phi-\Psi] \right\} \] where ${\rm Stat}$ denotes evaluation at a solution of the stationarity condition with respect to $\Psi$. This variational composition applies to both local and nonlocal Schwinger-Keldysh effective actions in nonequilibrium quantum field theory. We illustrate its linear and nonlinear realizations through quadratic theories and general time independent effective actions, respectively.