We derive the complete set of positivity bounds for the leading-twist parton distribution functions (PDFs) of a spin-$3/2$ hadron for the first time. This work generalizes the Soffer bound, a fundamental constraint for spin-$1/2$ nucleons, to quark and gluon distribution functions in higher-spin systems. Expressing the antiparton-hadron scattering amplitudes in terms of the PDFs and the spin density matrix, we establish the connections between the PDFs and the scattering amplitudes in the tensor product space of the parton and hadron spins. Moreover, we obtain the definitions of the PDFs in terms of the helicity amplitudes. Positive definiteness of the scattering amplitude matrix yields a set of inequalities that define the physically allowed parameter space for the helicity amplitudes and a set of constraints for the PDFs. The Cauchy-Schwartz inequality determines the constrains between the PDFs and generalized parton distributions.

Nonperturbative corrections to hadronic observables represent a critical obstacle to increasing accuracy at colliders. Long taken to scale simply as $1/Q$, where $Q$ is the center-of-mass scattering energy, recent work has opened the path toward calculating the anomalous dimension that modifies that scaling. A priori, the problem is complex, requiring a resummation involving arbitrary numbers of large-angle and low-energy gluons. Within a specific framework for kinematic recoil, we show that it reduces to a simple exponential for key observables like the thrust, $C$-parameter and energy correlators. This simplicity holds for a specific hadron-mass scheme, and also even beyond the two-jet limit.

We study the behavior of the conformal block expansions of scalar five-point Lorentzian conformal correlators in the limit where multiple cross ratios approach zero. Since this limit is controlled by intermediate operators with large spin, we use it to study the large spin expansion of the operator product expansion (OPE) coefficients involving these operators. By imposing bootstrap assumptions such as analyticity of the correlators, we derive an infinite set of new constraints on the large spin behavior of OPE coefficients involving multiple spinning operators. We also show that for the case of $l=0$, these constraints can be trivialized to all orders in $1/J$ by identifying a pattern in the coefficients.

In this paper we analyze the phases that dominate the microcanonical ensemble at various energies in the D1-D5 CFT, which is dual to type II string theory on ${\mathrm{AdS}}_3\times S^3\times T^4$. We focus on black hole solutions, and on the dependence of the phase structure on the ratio of the size of the torus to the Anti-de Sitter (AdS) scale; as small localized black holes (with horizon topology $S^8$) grow, they can start to fill the $S^3$ or the $T^4$ or both, and we analyze the general aspects of the transitions between the various phases of uniform and nonuniform black holes, incorporating known solutions and discussing the properties of additional unknown solutions. Some features of the transitions between these phases are similar to higher dimensional AdS spaces, while other features are different. We provide evidence that when the torus is much larger than the AdS radius, there is a large range of energies where the typical states are a novel phase, described by a lattice (in the $T^4$ directions) of black holes with horizon topology $S^5\times S^3$. In this phase the entropy is linear in the energy, with a coefficient that is of order the AdS radius.

We find a large class of holographic solutions describing D4-branes wrapped on four-manifolds ${\mathcal{M}}_4$ with constant curvature leading to gravity duals of supersymmetric quantum mechanics in the IR via twisted compactifications. The manifolds ${\mathcal{M}}_4$ considered here are four-dimensional spheres and hyperbolic spaces, products of two Riemann surfaces, and Kahler four-cycles. The solutions are obtained from the maximal gauged supergravity in six dimensions with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)⋉{\mathbb{R}}^4$ gauge groups. These gauged supergravities can be embedded in type IIA theory via consistent truncations on $H^{p,q}\times {\mathbb{R}}^{5-p-q}$ and $H^{p,q}\times {\mathbb{R}}^{4-p-q}\times S^1$, respectively. The solutions take the form of $t\times {\mathcal{M}}_4$-sliced domain walls interpolating between locally flat domain walls and singular geometries in the IR. Upon uplifted to type IIA theory, many solutions admit physical IR singularities and could holographically describe supersymmetric quantum mechanics arising from twisted compactifications of D4-branes on ${\mathcal{M}}_4$.

We present remarkably simple covariant expressions for the graviton and ghost propagators in anti–de Sitter (AdS) spacetime valid in any spacetime dimension. In gravity there is a two-parameter family of covariant gauge-fixing conditions and the simplification occurs for a special choice of these parameters. In this gauge the graviton propagator satisfies ${\nabla }^{\mu }\mu {\nabla }^{\nu }\mu G_{\mu \nu ,{\alpha }^{\prime }{\beta }^{\prime }}(\mu )=0$, where $\mu$ is the geodesic distance between two points, and this condition implies an improved infrared behavior. This gauge choice is not possible in flat spacetime.

We investigate whether spontaneous symmetry breaking can persist up to arbitrarily high temperature in ultraviolet-complete quantum field theories in four spacetime dimensions. We focus on completely asymptotically free models with gauge group $\mathrm{SU}(N_{c1})\times \mathrm{SU}(N_{c2})$ and two complex scalar fields, each transforming in the fundamental representation of one gauge factor and singlet under the other. The scalar potential contains quartic self-interactions together with a negative portal coupling between the two sectors. In the Veneziano limit, this class of theories was previously shown to admit fixed-flow trajectories for which one scalar acquires a negative thermal mass at asymptotically large temperature, leading to symmetry nonrestoration. Here we extend that analysis to finite numbers of colors and flavors. We derive the finite-$N$ fixed-flow equations, compute the leading $1/N$ corrections to the large-$N$ solutions, and solve the full finite-$N$ system numerically. We find explicit finite-$N$ benchmark theories for which the scalar potential remains bounded from below, the gauge sector is asymptotically free, and one scalar thermal mass stays negative at arbitrarily high temperature. This provides an explicit perturbative example of infinite heat order in a four-dimensional ultraviolet-complete quantum field theory with a finite field content.

We study Dirac fields on ${\mathrm{AdS}}_n$ in both global and Poincaré charts and, for each mass window, we classify the boundary conditions at conformal infinity that ensure the existence of advanced and retarded propagators. We distinguish the well-known MIT–bag class from a generalized family, thereby extending to arbitrary dimensions the procedure initiated in [D. S. Blanco, J. Math. Phys. (N.Y.) 64, 032301 (2023).]. As in the scalar case, we show that suitable generalized boundary data can support bound states. In four dimensions, we work out two explicit examples: (i) the MIT case, for which we construct the advanced/retarded propagators and the two-point function of the associated ground state and (ii) a representative generalized boundary condition, for which we construct the propagators and exhibit a normalizable bound state.

We construct symmetry topological field theories using the sandwich construction of Pulmann-Ševera-Valach that manifest the center symmetries of Chern-Simons theory and Yang-Mills theory as well as general relativity in the MacDowell-Mansouri formulation. The “filling” of the sandwich is an Alexandrov-Kontsevich-Schwarz-Zaboronsky sigma model whose target space is a Weil algebra, augmented with discrete degrees of freedom given by a choice of topological boundary condition.

We calculate the resummed perturbative free energy of $\mathcal{N}=4$ supersymmetric Yang-Mills in four spacetime dimensions (${\mathrm{SYM}}_{44}$) to order ${\lambda }^{5/2}$ in the ‘t Hooft coupling at finite temperature and zero chemical potential. All infrared divergences cancel when we include contributions from ${\mathrm{SYM}}_{44}$ ring diagrams and the final result is both ultraviolet and infrared finite. Our result has special significance since order ${\lambda }^{5/2}$ is the highest order calculation that can be done with perturbation theory, because there are nonperturbative effects associated with the magnetic mass scale that come into play at order ${\lambda }^3$. We compare results obtained with regularization by dimensional reduction (RDR), which preserves supersymmetry, and canonical dimensional regularization (DR). We also compare with a generalized Padé approximant constructed by matching the weak coupling result at order ${\lambda }^2$ and the large $N_c$ strong coupling result at order ${\lambda }^{-3/2}$. Finally we make a comparison between our result and the QCD free energy and show that ${\mathrm{SYM}}_{44}$ has better convergence properties.

Time-delay interferometry (TDI) is essential for space-based gravitational wave (GW) missions, as it suppresses laser frequency noise and achieve the required sensitivity. Beyond the standard Michelson configuration, a variety of second-generation TDI schemes have been proposed, each utilizing different combinations of interspacecraft laser links. In this work, we conduct a comparative study of several representative TDI configurations with different time spans, and show that while their (quasi)orthogonal channels are highly correlated, their performance in data analysis can differ among these schemes. In the low-frequency regime, the performance of different TDI configurations are nearly identical. Their distinctions emerge primarily at high frequencies, where the GW wavelength becomes comparable to the arm length. In this regime, shorter TDI time spans with minimal null frequencies facilitate more accurate waveform modeling and parameter recovery in frequency domain. In contrast, configurations with longer time spans and more null frequencies, such as the Michelson, are more susceptible to frequency aliasing and waveform modulation effects, which degrade inference accuracy. However, if signal modeling and analysis are performed in the time domain, the optimal science channels of these TDI configurations exhibit consistent performance in parameter inference. Considering the usability in both frequency and time domain, the short-span PD4L scheme, which exhibits minimal nulls and superior performance in high frequencies, emerges as a promising candidate for future space-based GW mission designs.

Black-hole uniqueness, i.e., the statement that all stationary vacuum black holes in the universe are described by the Kerr solution, is expected to break in theories beyond general relativity. This breaking can take a particularly strong form, if several branches of black-hole solutions beyond the Kerr solution coexist. We find an example of a theory that exhibits such strong breaking. In this theory, a cubic coupling of a scalar field to the Gauss-Bonnet invariant triggers black-hole scalarization through a nonlinear instability of the Kerr solution. At large spin, curvature-induced and spin-induced scalarization mechanisms compete at fixed sign of the coupling. This results in a rich phase structure of black-hole solutions and continuous as well as discontinuous transitions between the different branches of black holes.

A gauge-theoretic framework for spacetime and gravitation is proposed, in which a Cartan chronon field breaks the symmetry between space and time, enabling the emergence of temporality within a fundamentally Euclidean setting. Based on a Spin(4) gauge structure, the theory provides a real-valued formulation of chiral spacetime, wherein the effects typically attributed to dark matter may instead be accounted for by the dynamics of gravitation. New results are presented that are relevant to a broad range of phenomena, including cosmology, large-scale structure, gravitational waves, black holes, and potential signatures accessible to laboratory experiments.

Quadratic gravity is a well-motivated extension of general relativity (GR) wherein the Einstein-Hilbert action is augmented by quadratic curvature terms. This theory is equivalent to GR in an effective-field-theory framework, while the two theories are different at the nonperturbative level. As we have recently shown, black holes in quadratic gravity have a rich linear response, including extra scalar, vector, and tensor quasinormal modes that can be excited in physical processes, even when the stationary solution is the same as in GR. Here, by studying the gravitational-wave emission from point particles plunging into a Schwarzschild black hole in quadratic gravity, we show that observable deviations from GR are exponentially suppressed in the GR limit. This provides a nonperturbative realization of the equivalence between quadratic gravity and GR predicted in the effective-field-theory framework.

We numerically construct asymptotically extremal black holes through the nonlinear evolution of a charged scalar field. Our procedure—which extends the work of Murata-Reall-Tanahashi [Classical Quantum Gravity 30, 235007 (2013)] to include charged scalar dynamics—involves the fine-tuned scattering of wave packets within an initially superextremal Reissner-Nordström spacetime. The resulting extremal solution develops an event horizon along which the energy density diverges and the charge density approaches a constant (i.e., the horizon forms with “hair”). We investigate this behavior from the perspective of critical phenomena in gravitational collapse, giving evidence that dynamical extremal black holes act as universal threshold solutions modulo this family-dependent hair. As in the linear instability of fixed extremal backgrounds, the scalar field decays outside the dynamical extremal horizon. But just inside the horizon, the scalar curvature appears to develop unbounded growth. This implies that near-threshold solutions without a black hole could develop correspondingly large curvatures visible from future null infinity.

Recent pulsar timing array datasets provide compelling evidence for a nanohertz gravitational-wave background, but robust detection requires characterizing statistical fluctuations of the Hellings-Downs (HD) correlation expected from a finite population of discrete sources. Building on the variance calculation of Allen [Variance of the Hellings-Downs correlation, Phys. Rev. D 107, 043018 (2023)], we derive the third central moment (skewness) of the HD correlation for a single unpolarized point source and an ensemble of many interfering point sources in the confusion-noise regime. To isolate the intrinsic non-Gaussianity of the background, we extend the pulsar-averaging formalism to third order by introducing a three-point-averaged correlation function, which allows us to define the cosmic skewness. We find that the skewness remains nonzero in the large-source-number limit and is controlled by a new geometric three-point function. These results suggest that incorporating higher-order moments could provide additional information on source discreteness beyond standard Gaussian analyses.

We study the spacelike Kasner singularity of spherically symmetric, static, and asymptotically flat black holes in Einstein gravity minimally coupled to a massless scalar with a suitable self-interacting scalar potential. We focus on how the asymptotic information such as the mass and scalar charge affect the properties of the Kasner singularity, including the Kasner exponents. We show how a nontrivial integration constant can be extracted from the near-singularity geometry and find a general pattern that this integration constant asymptotes to a linear combination of the mass and scalar charge at large mass limit. We also find that there may be a black hole upper bound on the maximum surviving time of a massive particle inside such a black hole before it falls into the Kasner singularity, and the Schwarzschild black hole saturates this bound.

Simulation-based inference provides a powerful framework for Bayesian inference when the likelihood is analytically intractable or computationally prohibitive. By leveraging machine-learning techniques and neural density estimators, it enables flexible likelihood or posterior modeling directly from simulations. We introduce residual neural likelihood estimation (RNLE), a modification of neural likelihood estimation (NLE) that learns the likelihood of non-Gaussian noise in gravitational-wave detector data. Exploiting the additive structure of the signal and noise generation processes, RNLE directly models the noise distribution, substantially reducing the number of simulations required for accurate parameter estimation and improving robustness to realistic noise artifacts. The performance of RNLE is demonstrated using a toy model, simulated gravitational-wave signals, and real detector noise from ground based interferometers. In the presence of loud non-Gaussian transients, we find that RNLE can improve robustness of parameter recovery when trained on appropriately constructed datasets. We further assess the stability of the method by quantifying the variability introduced by retraining the conditional density estimator on statistically identical datasets with different optimization seeds, referred to as training noise, and investigate evidence-weighted combinations of independently trained RNLE realizations as a diagnostic of this variability. An implementation of RNLE is publicly available in the sbilby package, enabling its deployment within gravitational-wave astronomy and a broad range of scientific applications requiring flexible, simulation-based likelihood estimation.

We study generalized Proca theories inspired by the recent regularized Proca theory of four-dimensional Gauss-Bonnet gravity. By abandoning the rigid constraints typically imposed by specific regularization schemes, we treat the coefficients of the terms in the action as free parameters. This approach uncovers a broader solution space that admits static and spherically symmetric black hole solutions characterized by primary hair, where, surprisingly, the cosmological constant arises naturally as a constant of integration even in the absence of a bare cosmological term.

In this article, we extend the numerical studies developed in [Periodic analogues of the Kerr solutions: A numerical study, Classical Quantum Gravity 40, 175010 (2023).] to construct periodic stationary axisymmetric solutions containing multiple horizons in each fundamental domain. As a direct application, we consider periodic stationary axisymmetric solutions with two identical equidistant counterrotating horizons. These solutions can be parametrized by the period $L$, the mass $M$, and the absolute value of the angular momentum $|J|>0$. We provide strong numerical evidence for the existence of such configurations, without any restriction in terms of the distance between horizons. This is in sharp contrast with the nonzero total angular momentum case, as it was recently established in [Static vacuum $3+1$ black holes that cannot be put into stationary rotation, Classical Quantum Gravity 42, 085008 (2025).] that static single-horizon periodic solutions cannot be put into rotation if $L<4M$. It is shown that these solutions do not have any struts on the axis, and it is also explicitly shown that, by taking nonequidistant horizons, struts develop between the black holes. Other global properties of the solutions are also presented.