Papers

We investigate the implications of causality and positivity for the tidal Love numbers of gravitating objects. We work within the framework of point-particle effective field theory, where the Love numbers correspond to the Wilson coefficients of operators constructed from the curvature tensor and its derivatives. For simplicity, we focus on the quadrupolar gravito-electric sector, which provides the leading contribution to tidal deformability. We show that requiring the tidal response to be retarded and to decay at high frequencies, together with the assumption of passivity, leads to nontrivial bounds on the Love numbers. These bounds delineate an allowed region in the parameter space of the effective theory and apply to any localized object. In particular, we study their application to neutron stars. We compute the dynamical Love numbers through fourth order in the frequency expansion for a representative set of polytropic and tabulated neutron-star equations of state and show that, in the low-compactness regime, the bounds translate into constraints on the first oscillation mode of the star. Importantly, these constraints are conceptually independent of the stability and thermodynamic conditions commonly imposed in the literature. While our focus is primarily on conservative systems, we also discuss how the bounds are modified in the presence of dissipation. Our results lay the ground for a systematic framework to derive bounds on compact objects from fundamental principles.

We study entanglement entropy in a certain ansatz of matrix quantum mechanics (MQM) wavefunctions which behave as generating functionals for a planar 't Hooft expansion. We argue that these 't Hooft diagrammatics can directly probe aspects of the topology of the bulk dual, such as the contractibility of a thermal or replica $S^1$ cycle. Our argument relies on treating 't Hooft diagrams as a non-perturbative definition of off-shell string theory worldsheets in which contractibility of replica cycle leads to worldsheets punctured by a conical deficit (as first described by Susskind and Uglum). We describe how a deconfinement transition in the MQM is tied to the exchange of dominant topologies, as well as to a candidate description of open string 'edge modes' of Susskind and Uglum. Lastly, we study toy models of black hole evaporation and show that the boundary planar expansion itself diagnoses the exchange of dominance between the disconnected topology and replica wormhole topology, without ensemble averaging and without independently postulating which bulk saddles should be included.

We make use of unique properties of scaling functions to estimate the chiral phase transition temperature and corresponding universal critical parameters of this phase transition directly from (2+1)-flavor QCD simulations with highly improved staggered fermions on lattices with temporal extent $N_\tau=8$. Working with an improved chiral order parameter for quantifying chiral symmetry breaking, we analyze the finite-volume dependence of this observable for a wide range of lattice volumes and light quark masses, and quantitatively estimate the deviations from the expected universal scaling behaviour as a function of the light-to-strange quark mass ratio.

We construct and analyse orientifold descendants of a six-dimensional type IIB $\mathbb Z_{12}$ quasicrystalline orbifold. The parent background is defined by a Narain-lattice automorphism that is not crystallographic on the geometric torus. We determine the closed-string spectrum and twisted-sector orbit structure, construct a compatible unoriented projection, and compute the Klein bottle, annulus and Möbius strip amplitudes. Tadpole cancellation selects boundary orbits that admit a partially T-dual description as D7-branes at angles and fixes the Chan-Paton gauge group and massless spectrum. The resulting supersymmetric six-dimensional vacuum satisfies the irreducible anomaly constraints, its reducible anomaly polynomial factorizes through the Green-Schwarz mechanism, and its anomaly lattice obeys the Kim-Shiu-Vafa string-probe bound. We also construct a Brane Supersymmetry Breaking descendant with a perturbatively tachyon-free rigid branch, and a freely acting five-dimensional orientifold whose two decompactification limits reproduce a geometric type IIA $\mathbb Z_3$ orientifold and an antisymmetric type IIB $\mathbb Z_4$ orientifold. These examples show that quasicrystalline closed-string backgrounds can admit controlled perturbative open-string completions with non-trivial boundary and crosscap sectors.

The out-of-time-order correlator (OTOC) has emerged as an important diagnostic for quantum information scrambling and a key signature of quantum chaos. In this work, we discuss out-of-time-order correlators, analytically and numerically, for the so-called Volcano potentials. This family of potentials parametrically interpolates between bounded wells and confining walls, and includes Pöschl-Teller as a specific case. Through a combination of numerical diagonalization and semiclassical analysis, we investigate various regimes of the potential parameter regimes containing regions of both positive and negative curvatures. Moreover, we demonstrate in this case that short-time exponential growth of the OTOC does not necessarily signal global quantum chaos; instead, it correlates with the sampling of negative curvature regions by excited states.

T-branes have been argued to provide a consistent uplift to de Sitter vacua in the context of the LARGE-volume scenario of type IIB string theory. We point out that this construction suffers from a serious control problem: the string-frame volume is bounded from above by a number that depends only on the topology of the Calabi-Yau orientifold and is often $\mathcal{O}(1)$ or smaller. This observation immediately rules out controlled de Sitter vacua in many models with $h^{1,1}=2$ if the non-perturbative superpotential is generated by D3-brane instantons. We give evidence that similar conclusions apply for $h^{1,1}>2$ and show this explicitly for two models with $h^{1,1}=4$. Our volume bound is seemingly less severe in models where the non-perturbative superpotential is generated by gaugino condensation. However, we study $\mathcal{O}(600)$ such models and find that, although de Sitter solutions with large volumes are naively possible there, they suffer from uncontrolled warping corrections whose volume suppression is cancelled by other factors, in particular large charges. We also observe that the models with the smallest warping corrections within our set have very small tadpoles and at the same time require a fine-tuned string coupling and flux superpotential, which may indicate an additional problem with the axio-dilaton/complex-structure-moduli stabilization. Finally, we point out an independent challenge related to the stabilization of the brane moduli. Our various results lead us to conclude that it is unlikely that the scenario of T-brane uplifting can be realized in string theory in a self-consistent manner.

We study the topological band theory of quantum Hall systems in which the adiabatic flux parameters of an external gauge potential form a high-dimensional manifold. This situation arises both for strongly correlated matter on spatial Riemann surfaces of genus $g > 1$, as well as in the formal study of matter on compact oriented manifolds of dimension $4\ell+2 = 2p$ coupled to $p$-form gauge potentials. In these cases, the underlying topological invariants defined over the parameter space are significantly richer than the low-dimensional (i.e., two-dimensional) case and involve both the curvature (i.e., first Chern class) as well as higher order curvature invariants. These higher curvature invariants correspond to topologically protected contributions to Kubo-like formulae, constructed from correlation functions of the physical current operators. We illustrate these general considerations with an explicit example from hyperbolic band theory based on the genus-two Bolza Riemann surface, a case which has recently been simulated on a synthetic-dimension platform.

We show that the large-$z$ behavior of massive higher-spin particles under all-line transverse shifts is controlled by the helicity magnitude rather than the total spin. The apparent additional $z$ growth of nonextremal higher-spin wavefunctions is removed by unified Ward identities acting independently on each vector index. To expose this structure, we embed a four-dimensional massive momentum and its mass into an auxiliary null five-vector, whose fifth-current components characterize the breaking and restoration of the massless Ward identities. These identities determine the fixed-helicity large-$z$ scaling and yield a helicity-resolved constructibility criterion valid for arbitrary spin. Provided the stripped kinematic tensor remains finite in the massless limit, increasing the total spin does not by itself worsen constructibility, and amplitudes with nonnegative coupling dimension are constructible for all helicity configurations at five points and beyond.

Black hole quasinormal modes (QNMs) provide a window into the underlying structure of black holes and the environments in which they arise. QNMs have particularly rich dynamics in coupled systems beyond general relativity, in which they are known to undergo avoided crossings, resonant excitation, and mode reconnections. Recent work has shown that reconnecting QNM trajectories can trace out a distinctive double spiral structure in the complex frequency plane. In this work, we study this phenomenology in a concrete model of perturbed dynamical Chern-Simons (dCS) theory, as well as in a minimal toy model. In the former, we characterize the exceptional points, avoided crossings and reconnections for several values of the perturbation parameters, and find that the limiting frequency of the double spiral endpoints is independent of the perturbation strength. We compute the excitation factors and find that they follow the scaling characteristic of a resonance between the scalar and gravitational modes. To determine whether these phenomena depend on the specific features of dCS, we construct a toy model of coupled degrees of freedom with square potential barriers, and find that we can reproduce the avoided crossings and reconnections, indicating that these phenomena can occur more generally in coupled systems and are highly sensitive to the system parameters.

The primordial scalar power spectrum provides a powerful window onto early-universe physics, including a broad class of inflationary scenarios. These models often predict a characteristic scalar spectral index $(n_s)$, nonzero running $(\alpha_s)$, or more general deviations from a pure power-law form. We find that freeing the number of light relic species $(N_{\rm eff})$ and the sum of the neutrino masses $(\sum m_\nu)$ broadens the $n_s$ error contours enough that key early-Universe models are no longer excluded. In particular, while both Starobinsky inflation and the Bi-thermal Big Bang model are ruled out at about the 95% confidence level in the six-parameter $\Lambda$CDM model, we find that in the nine-parameter $\Lambda{\rm CDM} + \alpha_s + N_{\rm eff} + \sum m_\nu$ model, CMB data from Planck, ACT, and SPT (CMB-PAS) combined with DESI DR2 give $n_s = 0.9758 \pm 0.0064$ and $\alpha_s = 0.0080 \pm 0.0064$, consistent with both models. Future CMB facilities will sharply improve constraints on $n_s$, $\alpha_s$, and, more generally, the binned primordial power spectrum $\mathcal{P}(k)$. For example, CMB-PAS constrains $e^{-2\tau}\mathcal{P}(k = 0.2\,{\rm Mpc}^{-1})$ to 0.5%, while SO-like and CMB-HD-like surveys would tighten this to 0.1%; CMB-HD would also extend this measurement to smaller, previously unprobed scales, constraining $e^{-2\tau}\mathcal{P}(k = 30\,{\rm Mpc}^{-1})$ to within a factor of ten. We release our forecast code and update the public CMB-HD likelihood and Fisher codes to support CLASS in addition to CAMB.

The general local solutions to complexified Type IIB supergravity which are invariant under the complex Lie superalgebra $F(4)$, and which were derived and classified in arXiv:2508.14959, are supplemented here by the construction of their flux potentials and field strengths. We then focus on the Type IIB$^\star$ real form of complex Type IIB supergravity, where we obtain solutions with spacetime metric of the warped product form $dS_{1,5}\times S^2\times\Sigma$. We systematically derive boundary and regularity conditions under which the $dS_{1,5}\times S^2\times\Sigma$ solutions can be analytically continued to regular $S^6\times S^2\times\Sigma$ solutions in Euclidean Type IIB supergravity. Using these results, we construct explicit global solutions. These solutions include explicit realizations of recent proposals for a holographic description of the polarized IKKT model, and we clarify the charges carried by these solutions. We also obtain novel solutions in the same regularity class with different brane charges.

The detection of gravitational waves in the low-frequency band (10 nHz to 1 micro-Hz) using inner solar system proof masses is severely limited by Newtonian gravity gradient noise (GGN) sourced by the asteroid belt. In this paper, we propose a novel detection concept that exploits the relativistic nature of gravitational waves to break the degeneracy between the signal and the asteroid GGN background. The non-relativistic motion of asteroids dominantly sources gravito-electric fields, with velocity suppressed gravito-magnetic components. Relativistic gravitational waves produce gravito-electric and gravito-magnetic components of equal magnitude. We propose detecting the gravito-magnetic component of low frequency gravitational waves using the Lorentz acceleration of test bodies. The measurement of this Lorentz acceleration is metrologically possible due to the fact that expected astrophysical sources of low frequency gravitational waves have considerably higher characteristic strains than the strains typically expected at higher frequencies. We show that this measurement allows for unambiguous extraction of the gravitational wave signal from the gravity gradient noise in a three satellite constellation. The gravito-magnetic measurement still requires a proof mass that is well isolated from non-gravitational noise. We propose the use of atom interferometers to serve as such a pristine inertial reference.

We present a new supersymmetric, non-extremal complexification of asymptotically $\mathrm{AdS}$ black holes, characterized by real charges and multiple complex horizons. We investigate whether these solutions define admissible supersymmetric saddles of the gravitational path integral by applying the Kontsevich-Segal-Witten (KSW) criterion, and compare the resulting gravitational constraints with the convergence conditions of the dual superconformal index. For most of the cases studied, the KSW criterion in the asymptotic region agrees with the index convergence, while the full bulk condition is more stringent and excludes saddles whose chemical potentials lie within the index-convergence domain.

Fuzzy-sphere regularization has recently emerged as a powerful framework for studying three-dimensional conformal field theories (CFTs). In this work, we exploit symmetry and Hilbert-space structures to substantially advance this framework. We develop an exact-diagonalization algorithm that resolves the full $\mathrm{SO}(3)$ rotational symmetry, reducing computational costs by factors of several hundred. For the three-dimensional Ising CFT, we identify around 100 primary operators, including a large number of previously unknown heavy scalar primaries up to scaling dimension $\Delta\approx16.5$. We also resolve the tension between previous fuzzy-sphere and bootstrap results regarding the parity-odd scalar primary. Furthermore, we identify a branch of scalar primaries associated with $\phi^n$ operators in the $\phi^4$ Lagrangian description, beginning with the identity, $\sigma$, $\epsilon$, $\epsilon'$, and $\sigma'$. Their wave functions exhibit a semi-classical structure closely related to states invariant under area-preserving diffeomorphisms of the sphere. Finally, we show that critical points involving fractional quantum Hall states can be studied within a substantially reduced Hilbert space spanned by quasi-hole states of the corresponding model quantum Hall wave functions like the Laughlin state. This suggests a general strategy for exploring CFTs intertwined with topologically ordered phases.

We introduce Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics. The solution process is tracked through a persistent ledger that records assumptions, derivations, and computations. A central agent delegates tasks to specialized sub-agents, while independent agents verify both intermediate steps and the final result. This setup improves the traceability, reproducibility, and verification of computer-assisted calculations. Applying Solver Agent, we study global F-theory uplifts of Type IIB orientifolds and their S-fold generalizations. We establish sufficient conditions for Weierstrass models over projective threefolds with terminal $\mathbb{Z}_k$ quotient singularities ($k\in\{2,3,4,6\}$) to give $\mathbb{Q}$-factorial projective elliptically fibered Calabi-Yau fourfolds with isolated Gorenstein terminal quotient singularities. These geometries realize O3-planes and S-folds, where local D3-brane probes of the latter yield four-dimensional $\mathcal{N}=3$ superconformal field theories. Using stringy invariants, we derive fixed-point contributions to Hodge data and Euler characteristics, and show that these Euler corrections determine the localized D3-brane charges required for tadpole cancellation. We illustrate these results using toric hypersurface constructions, where a single three-dimensional polytope determines both the Type IIB Calabi-Yau threefold and the F-theory base; here, the orientifold double cover naturally forms a bisection of an alternative genus-one-fibered uplift with discrete $\mathbb{Z}_2$ gauge symmetry. Finally, we provide methods for toric computations and four-form flux analysis in four-dimensional $\mathcal{N}=1$ compactifications with non-abelian gauge sectors.

Standard-Model warm inflation (SMWI) makes QCD the microscopic origin of inflationary dissipation, so the real-time response of the gauge plasma enters the cosmological prediction. We show that a slowly relaxing gauge-helicity response cannot, in general, be absorbed into an effective friction coefficient and must instead remain dynamical. We therefore evolve the quark axial densities and a matched hard-helicity mode, with QCD sphalerons and an effective $2\leftrightarrow3$ channel generating both charge transfer and correlated stochastic sources in the full perturbation covariance system. The resulting backreaction is substantial but mainly indirect: gauge-helicity screening can reduce the warm dissipation ratio by an order-one fraction on the strong branch, while the $2\leftrightarrow3$ channel contributes only $0.2\%-0.7\%$ of the zero-density sphaleron friction directly, shifting the amplitude-normalized trajectory in both $n_s$ and $r_{\rm vac}$. The relevant trajectories, however, lack a parametrically broad hard-soft hierarchy and extend beyond strict linear response. The predictions should therefore be understood within the stated local Gaussian transport closure; a parameter-free Standard-Model (SM) result requires finite-affinity real-time $SU(3)$ drift, susceptibility, and noise kernels.

Lattice gauge theories are an important class of physical models with high-dimensional structured distributions that underpin first-principles calculations in particle, nuclear, and condensed-matter physics. Recent advances in generative modeling have opened new avenues for sampling Boltzmann distributions in lattice gauge theories, offering the potential to alleviate limitations of traditional Monte Carlo methods, including critical slowing down and topological freezing. However, generative samplers for lattice gauge theories are typically constructed in link space, where correlations become increasingly long-ranged toward weak coupling, posing a challenge for learning. Plaquettes provide a more natural representation, as the action is local in these variables. However, exact Bianchi constraints restrict them to a lower-dimensional manifold, complicating direct generative modeling. We introduce a multilevel normalizing-flow construction that samples directly in plaquette space while satisfying these constraints exactly. The key idea is a coarse-to fine factorization that transforms a globally coupled constraint problem into a sequence of local solves: at each refinement, every determined plaquette depends on at most four newly generated variables, while the size of the constraint problem remains independent of the lattice size. We validate the construction for $U(1)$ in two and four dimensions and for $SU(2)$ in two dimensions. Our multilevel Plaquette-Space Sampler (PSS) substantially outperforms link-space baselines, with the advantage increasing toward weak coupling, where the gauge coupling becomes small. This regime is particularly challenging for generative sampling and, in asymptotically free gauge theories, is relevant to continuum studies.

An infalling two-point function of a scalar field in a three-dimensional BTZ black hole, with one operator inserted in the exterior and the other inserted along a timelike geodesic, diverges when the infalling insertion point reaches the black hole singularity. In the boundary description, this divergence is tied to the exchange of double-twist operators rather than to the multi-stress-tensor sector that encodes curvature singularities in higher dimensions. We show that the inclusion of a tower of massive particles with Hagedorn growth gives rise to loop corrections that become important near the singularity, where they trigger a Hagedorn transition that renders the tree-level divergence untrustworthy. In the boundary theory, the corresponding tower of primary operators leads to a breakdown of the generalized free field description of the probe operator in the black hole state. In a large black hole, these corrections become important only near the singularity and remain exponentially suppressed at the horizon. The region where these corrections dominate is therefore parametrically separated from the horizon, as anticipated by the principle of black hole complementarity.

We study BPS states in the D1–D5 CFT through their fortuity, cycle structure, and probe response. Explicit fortuitous states with both long- and short-string geometries show that the cycle partition does not determine fortuity state by state. At large $N$, fixed-charge counting nevertheless selects a long string. In the open uncondensed region, an entropy-carrying exact non-graviton subspace concentrates on one cycle of winding $N-O(1)$. Assuming subexponential monotone dimension, the same holds for the harmonic fortuitous complement. Beyond the critical line, the free ensemble develops a short-string condensate. To test how this cycle structure appears in observables, we study finite-winding probes. The long-cycle scalar correlator approaches the extremal-BTZ response at fixed time, while finite winding is resolved at \(t=O(\sqrt N)\), the exact circle recurs at \(t=O(N)\), and states with the same cycle geometry remain distinguishable by their spectral weights.

For every pair of integers $0\leq k\leq N,$ and and every subgroup of $D_N\times\mathbb{Z}_2$, we construct the nonnegative symmetric Grassmannian, which is the subspace of the nonnegative Grassmannian fixed under that group, where the dihedral part acts on columns (with a sign correction to keep nonnegativity) and the $\mathbb{Z}_2$ factor exchanges a space with its orthocomplement (again, with a sign correction). This construction generalizes the earlier constructions of \cite{Karpman2018,Fraser2020,Shevchenko2025}. We study the geometry of this space. Then, when $k$ is further restricted to the range $[2,N-2]$ we also define a symmetric amplituhedron. We analyze its basic properties and its conjectural BCFW decomposition. The ABJM and reflected Lagrangian amplituhedra are the special cases corresponding to the groups $\{1\}\times\mathbb{Z}_2,$ and the group generated by a reflection combined with the exchange,

The pole structure of string correlators in AdS$_3$ encodes essential information about the AdS$_3$/CFT$_2$ duality. The corresponding residues for spectrally flowed three-point functions have been extracted from their exact expressions and shown to match the predictions of the holographic CFT. Away from the tensionless point, the latter is defined perturbatively in terms of a deformed symmetric orbifold. For $n$-point functions, this has so far only been achieved for a specific subset of poles and employing free-field techniques. Here we develop an alternative approach. We show that, starting from the localization properties of worldsheet correlators, one can solve the KZ equations on the corresponding locus and perform the integration over worldsheet moduli explicitly for any $n$ and for arbitrary values of the spectral flow charges. This provides a systematic framework for computing the remaining residues and, ultimately, for determining the full analytic structure of string amplitudes in AdS$_3$.

We study the asymptotic behavior of large-spin operators in conformal field theories by placing the theory on a pp-wave background. In this setting, three-point coefficients involving two large-spin operators and a light operator are mapped to thermal one-point functions on the pp-wave. We predict these one-point functions in the two complementary regimes of high- and low-temperature respectively, corresponding to a limit in which the twist scales with an appropriate power of the spin and the spin is parametrically larger than the twist, respectively. In particular, at high temperature we derive their asymptotic behavior using thermal effective field theory while at low temperature we obtain results that can be matched directly to predictions from the analytic bootstrap. We test these general results in free scalar theories. Finally, we solve the large-$N$ $\mathrm{O}(N)$ model numerically on the pp-wave, finding agreement with our predictions for both the one-point function and the free energy in the high- and low-temperature regimes.

Courant-Hilbert (CH) deformations unify broad classes of solvable stress-tensor flows including $T\bar{T}$ and root-$T\bar{T}$. However, a gravitational action that systematically yields such general deformations has remained unknown. In this Letter, we construct a two-dimensional massive gravity theory whose on-shell action reproduces the complete CH deformation. The gravity sector is defined via an arbitrary function of the eigenvalue ratio $y$ of the relative zweibein. To bypass the technical difficulty of directly eliminating the auxiliary zweibein, we reformulate the matter sector using a $2 \times 2$ spectral decomposition involving $y$ and a rank-one projector $K$. Sequentially solving the equations of motion–first for $K$ and subsequently for $y$–naturally maps the system onto the Russo-Townsend form of the CH flow. Our work extends Tolley's massive gravity formulation of $T\bar{T}$ flows to the CH landscape, providing a clear geometric mechanism for solvable stress-tensor flows.

We study collective charge excitations in three-dimensional $\mathcal{PT}$-symmetric nodal-ring semimetals (PTNRs) and their gapped counterparts (GNRs) in the presence of band tilt, together with Weyl semimetals (WSMs). Within a low-energy two-band description, we consider untilted systems as well as in-plane and axial tilts. Using the random-phase approximation, we obtain the density of states, Drude weights, dielectric functions, and plasmon dispersions at low doping and in the intrinsic limit. The mass gap and the two inequivalent tilt directions generate distinct Fermi-surface topologies and thereby control the formation and damping of plasmons. By comparing the collective modes with the particle-hole continuum, we identify the regimes in which plasmons remain well defined. We also calculate the response of untilted and tilted WSMs and contrast it with that of PTNRs and GNRs. The two classes of semimetals differ in the carrier-density dependence and isotropy of the plasmon frequency as well as in interband screening and their response to tilt. These differences reflect their distinct Fermi-surface geometries and interband structures. Our results establish how mass and tilt govern collective charge dynamics through their interplay with intraband spectral weight and interband particle-hole excitations.

An exotic linearised theory of superconformal gravity in $D=6, (4,0)$ superspace has been proposed by C.M. Hull. In this note we discuss the bosonic sector of this model in topologically non-trivial spaces. Roughly speaking, Hull's model can be thought of as a square of the $H=dB$ theory, although not all Hull fields can be so presented. We also briefly discuss the form sector of $D=11$ supergravity.

Loop Quantum Cosmology (LQC) replaces the big bang singularity of the homogeneous universe by a bounce, usually described by the modified Friedmann equation $H^2=\rho(1-\rho/\rho_c)/(3M_p^2)$. We show that this background dynamics follows from a local cuscuton effective theory, whose scalar equation is a constraint rather than a wave equation. One way to establish this is to write the cuscuton in terms of an angular coordinate $\theta$, identified with the LQC polymerization angle $2\lambda b$. Its constraint gives $H\propto\sin\theta$, while the Einstein constraint gives $\rho=\rho_c\sin^2(\theta/2)$, exactly reproducing the LQC bounce. To our knowledge, this is the first closed-form, local, generally covariant realization of the exact standard flat-FLRW LQC background dynamics for minimally coupled matter satisfying null energy condition, without introducing additional local dynamical degrees of freedom. A branchwise Legendre transformation establishes a canonical equivalence between the clock-gauge-fixed homogeneous mimetic system in the case of vanishing mimetic dust energy density and the cuscuton systems. It selects the constant-tension cuscuton coordinate $\Theta=\sin\theta-\theta$, while $\theta$ retains its interpretation as the LQC polymerization angle. This equivalence does not establish agreement of the inhomogeneous theories or their perturbations. The angular action also admits an explicit branched $f(K)$ representation, where $K$ is the mean extrinsic curvature of spatial hypersurfaces. The construction is therefore an effective covariant representation of the LQC holonomy correction, not a derivation from full loop quantum gravity.

We present the first calculation of the leading perturbative quantum chromodynamics (QCD) correction to the nonleptonic weak flavor-equilibration rate in dense quark matter. The computation is based on the Kadanoff-Baym kinetic equation and performed using real-time thermal field theory. The resulting QCD correction is both gauge invariant and fully finite. In particular, all soft and collinear divergences cancel after combining real and virtual corrections, in accordance with the Kinoshita-Lee-Nauenberg theorem. In the low-temperature regime relevant to compact-star dynamics, the correction enhances the tree-level rate by $30 - 40\%$ over the high-density range where perturbative QCD is applicable. The corrected rate improves on the tree-level result used in phenomenological calculations for more than three decades, providing a more accurate microscopic input for bulk-viscosity calculations in dense quark matter.

We study heterotic $G_2$ structures near a torsion-free standard embedding, to first order in $\alpha'$ and to all orders in formal deformations. The tangent connection is the Hull connection determined by the metric and flux. We construct a locally invertible family of differential operators relating the supersymmetry and instanton $BPS$ equations to the Euler-Lagrange equations of the heterotic superpotential. Using this comparison and the physical gauge symmetries, we construct a homological vector field locally formally conjugate to the Hamiltonian vector field of the superpotential. On a closed manifold in the fixed gerbe sector, the torsion equation implies vanishing of the leading flux. We prove ellipticity of the linearized deformation complex with mixed differential-order weights and construct a finite-dimensional cyclic $L_\infty$ model with a formal effective potential.

We consider the Sachdev-Ye-Kitaev model with $N$ Majorana fermions and interaction order $q$. For even $q\in \{2,4,...,N-2\}$, we give an elementary proof and show that the eigenvectors of the model are completely delocalized in all deterministic directions.

We investigate static, charged, asymptotically flat black holes in logarithmic nonlinear electrodynamics (LNED) within the $(Q,\epsilon)$ parameter space. We distinguish three phase structures: the horizon geometry, the background circular null orbits, and the circular photon orbits of the effective optical geometry. All share a zero-radius boundary $Q_{nc}(\epsilon;M)=\gamma M^{2/3}\epsilon^{1/6}$, but possess distinct critical structures: the extremal curve $Q_{ext}(\epsilon;M)$ and the background merger curve $Q_{m}(\epsilon;M)$ both terminate at the bifurcation point $(Q_{b},\epsilon_{b})$, located at $r=0$. In contrast, the effective photon-orbit merger curve $Q_{m}^{ph}(\epsilon;M)$ does not pass through this point. For $\epsilon\ge\epsilon_{b}$, approaching $Q_{nc}$ shrinks the horizon to zero radius, resulting in black points with non-zero, quantum-corrected entropy. Their Hawking temperature vanishes at the bifurcation point and diverges for $\epsilon>\epsilon_{b}$, except when $\eta\delta=1$, where the temperature at the bifurcation point also diverges. The background potential $V_{eff}^{bg}(r)$ develops an infinite barrier at $r=0$ without local extrema, acting as a perfect repeller. In contrast, the photon potential $V_{eff}^{ph}(r)$ is regularized with a maximum at a finite radius, acting as a partial reflector. Consequently, the black points retain photon spheres of finite radius. Away from $Q_{nc}$, for $\epsilon<\epsilon_{b}$, both geometries support horizonless structures above $Q_{ext}$; for $\epsilon\ge\epsilon_{b}$, only the optical geometry does so in the region $Q_{nc}<Q<Q_{m}^{ph}$. Non-radial geodesics are blocked from the singularity and can form metastable bound states, while radial geodesics either reach $r=0$ or escape to infinity. The critical impact parameter encodes both gravitational and optical-geometry effects, probing the distinct phase structures.