Papers

The LUX-ZEPLIN (LZ) Collaboration recently reported one event consistent with a $248$ keV nuclear recoil in a $2.84$ tonne-year exposure, with a maximum local significance of $3.4\sigma$ and a global significance of $2.6\sigma$. We investigate whether the dark matter (DM)–nucleon interactions favored by this high-energy event can arise from particle DM models that simultaneously reproduce the observed relic abundance and satisfy indirect-detection constraints. Using the published LZ efficiency and operator significances, we show that elastic spin-independent (SI) scattering poorly explains an isolated high-energy recoil because its spectrum is concentrated at lower energies, whereas elastic spin-dependent (SD) $\mathcal{O}_4$ scattering remains viable. Endothermic scattering instead naturally suppresses the low-energy rate and shifts the recoil spectrum toward the observed energy. A thermal pseudo-Dirac fermion with an off-diagonal vector interaction provides a simple realization of this mechanism. For $m_\chi\simeq1$ TeV, the relic-density requirement predicts $\sigma_N\simeq6.5\times10^{-43}\,\mathrm{cm}^2$, while a splitting $\delta\simeq297$ keV shifts the recoil spectrum into the LZ event region. Present-day indirect-detection signals can be strongly suppressed because freeze-out proceeds mainly through coannihilation, while the excited state is depleted at late times. A thermal Higgsino provides a more predictive realization: its relic abundance fixes the mass near $1.1$ TeV, while a splitting $\delta\simeq 377$ keV is required to reproduce the event. This interpretation is testable through the associated gamma-ray line signal. Overall, combining direct detection, relic density, and indirect detection significantly restricts the viable interpretations of the LZ event and provides concrete targets for future searches.

We present a systematic study of the transition form factors for the semileptonic decays $D\rightarrow Pe^{+}v_{e}$ and $D\rightarrow P\mu^{+}\bar{v}_{\mu}$ using QCD light-cone sum rules with chiral currents, with emphasis on the nonperturbative structure of the pion. The distribution amplitudes of the meson $\pi$, including twist-2 and higher-twist components, are analyzed and incorporated in our computation, employing both Gegenbauer polynomial expansions and the Basis Light-Front Quantization (BLFQ) method, where the latter yields a distribution that rapidly converges to the asymptotic form. Two relations linking transition form factors are derived and found to be consistent with the chiral symmetry of QCD. Our numerical predictions for the $D$-to-pion form factors agee well with BES\uppercase\expandafter{\romannumeral3} measurements and lattice QCD calculations. Furthermore, the differential decay widths obtained thereby for the $D$-to-pion decay also show consistency with the BES\uppercase\expandafter{\romannumeral3} data in the high-momentum-transfer ($q$) region with the $q^{2}>1\ \rm{GeV^2}$, implying new opportunities for the precise extraction of the CKM matrix element and the exploration of physics beyond the Standard Model.

Spin models with a given symmetry are easier to sample than scalar theories with the same symmetry on a lattice, as the constrained nature of spin variables enables cheap heat-bath updates. However, this constraint suppresses radial fluctuations, and consequently, spin models cannot be used to study the phenomena of spontaneous symmetry breaking, such as the Higgs phenomenon. To address this, we propose a class of scalar potentials based on Gaussian Mixture Models (GMMs) that are as easy to sample as spin models with a given symmetry. These potentials can be designed to belong to the same universality class as the theory of interest, thereby reproducing its critical properties while enabling efficient sampling. We construct such models for global $\mathbb{Z}_2$ symmetry, $U(1)$ gauge symmetry, and disordered systems. We also verify by numerical experiment that the case of $\mathbb{Z}_2$ symmetry in two dimensions lies in the two-dimensional Ising universality class.

Topological defects are ubiquitous in physics, arising from condensed matter physics to the early universe. Although there exist many universal scaling laws for correlations between topological defects, such as Porod scaling, the fingerprint of topological defect cores has remained largely unexplored. Here, we discover a universal scaling law in the region $k>1/\xi$, where $\xi$ is the healing length of the topological defects, taking the scaling of the form factor $S_f \propto k^{-(d+p+2)}$, where $d$ is the spatial dimension and $p$ is the defect codimension. We analytically prove that this exponent originates from a universal V-shaped cusp at the defect core and is independent of the underlying system and dynamics. Numerical simulations verify this scaling law in four typical frameworks: the time-dependent Ginzburg-Landau and Gross-Pitaevskii equations in the weak-coupling regime, the gauge/gravity duality model in the strong-coupling regime, and the Klein-Gordon equation in the Friedmann-Robertson-Walker background in cosmology. Our work provides a new probe for studying topological defects in systems ranging from superconductors to cosmological phase transitions.

We study the partition functions of Wess–Zumino–Witten (WZW) models with compact connected simple Lie group manifolds that are not simply connected. Starting from the modular-invariant partition function of Felder–Gawędzki–Kupiainen (FGK), we derive a localization formula, which can also be obtained directly by supersymmetric localization of the corresponding supersymmetric WZW model. Our results reveal a variety of topological effects associated with the nontrivial topology of the target group. In particular, the Wess–Zumino amplitude is governed by FGK cocycles, while the fermion Pfaffians exhibit global anomalies associated with the holonomies of Pfaffian line bundles, captured by relative Rochlin invariants. Together, these results provide a unified description of the topological contributions to the semiclassical localization of WZW models with non-simply connected target groups.

We study an infinite family of strongly coupled four-dimensional $\mathcal N=2$ superconformal field theories (SCFTs) distinguished by a trivial Higgs branch, known as the $(A_2,D_{3m+1})$ Argyre-Douglas theories. We propose that their associated vertex operator algebras (VOAs) are the doublet algebras $\mathcal A(4m+2)$, an infinite family of non-rational vertex operator superalgebras with a remarkably simple strong generating set of only three fields. We provide several highly nontrivial checks of this proposal. In particular, we reproduce the four-dimensional conformal anomalies $a$ and $c$ from the VOA and analytically prove the exact equality between the Schur index of the SCFT and the supercharacter of the VOA. A key ingredient is a diagonal-gauging realization of the $(A_2,D_{3m+1})$ theories in terms of two simpler building blocks, which makes the Schur-index computation tractable. Remarkably, we find that the resulting Schur index of the $(A_2,D_{3m+1})$ theory coincides with that of $\mathcal N=4$ $SU(2)$ Super-Yang-Mills theory, up to an overall prefactor and an appropriate identification of fugacities. We also discuss a generalization to the two-parameter family $(A_{2s},D_{(2s+1)m+1})$, whose members likewise have trivial Higgs branches and admit diagonal-gauging realizations. A particularly interesting subfamily is $(A_{2s},D_{2s+2})$, for which the four-dimensional conformal anomalies coincide, $a=c$. Our results reveal a systematic connection between Higgsless SCFTs, diagonal gauging, and strongly finite but non-rational vertex operator algebras.

We study the localization formula for the partition function of the Wess–Zumino–Witten (WZW) model on the torus for compact, connected, and simply connected simple Lie groups. We identify a missing factor in the original localization treatment of Murthy and Witten and show that it agrees with the result obtained from the Hamiltonian formulation. We trace its origin to the abelianization of the Wess–Zumino amplitude, which reduces to a flat Kalb–Ramond B–field holonomy in a Narain lattice CFT associated with the maximal torus. This establishes a direct relation between the localization result and the lattice description of the corresponding abelian theory. We further analyze the point–particle limit of the torus partition function, in which the WZW model reduces to quantum mechanics on the group manifold, and reproduce Frenkel's heat–kernel trace formula.

In positive degree, equivariant Gromov-Witten invariants of Calabi-Yau fivefolds are expected to admit an interpretation in terms of M2-branes, while we conjecture that constant maps are governed by the corresponding supergravity index. We make the first expectation precise by proposing a modular interpretation of M2-branes supported on several smooth curves meeting at an $n$-fold point. Together, the two pictures yield conjectural formulas for the Gromov-Witten invariants, which we translate into closed formulas for pointed and unpointed quintuple Hodge integrals. We show that these conjectures imply a K-theoretic Gromov-Witten/Pairs correspondence for local curves in degree one and link the generating series of constant maps to Donaldson-Thomas theory of points. We also prove the conjectures in two limits of the equivariant parameters. Along the way, we obtain new closed formulas for certain triple Hodge integrals.

Recently, we constructed analytical purely electric and purely magnetic black-hole solutions in Einstein–Euler–Heisenberg theory, while the corresponding dyonic solutions were obtained numerically \cite{Luo:2026srx}. Motivated by the recent analytical construction of a dyonic black hole at the special coupling locus $b=a/2$ \cite{Ahmed:2026ufj}, we revisit the general dyonic sector. We show that exact analytical dyonic black-hole solutions can be constructed for nonlinear couplings satisfying $2b>a$, without imposing the restriction $b=a/2$. The mass function is expressed in closed form in terms of the Lauricella hypergeometric function. In particular, our construction yields an exact dyonic solution for the Euler–Heisenberg coupling $b=7a/4$. The solution of Ref.~\cite{Ahmed:2026ufj} is recovered in the limiting case $2b\rightarrow a$.

We consider second quantized $1+1$ dimensional Dirac fermions with mass $m$ in background electric fields. This theory mimics the following situations. We consider two parallel capacitors with opposite directions of the electric field $E$ in them. The potential energy difference in one of them is equal to $V_0 > 2m$ and in the other to $V+V_0$, with $0<V<2m$. According to general physical understanding of the Schwinger effect, each capacitor separately will create pairs and there will be oppositely directed currents, which will not be equal to each other. The total current will not vanish. In this paper we show that this is too naive an observation: the limiting expectation value of the current operator, as $t\to +\infty$, is actually zero, if the above form of the potential with $0<V<2m$ is instantaneously turned on. The non-vanishing current is obtained only if $V>2m$. We also consider the same theory in the presence of the infinite wall and a deep well $V_0>2m$. We show that in such a potential the limiting expectation value of the current is zero in the Gaussian approximation. We discuss the relation of these observations to the Schwinger effet and to the decay of supercritical nuclei.

Motivated by the recent observation that rotating space-times at finite temperature can be described by particular flat, compact, orientable manifolds, which are different from $\mathbb T^4$, we catalogue all such 4-manifolds and their properties. There are in total 26 flat, compact, orientable 4-manifolds, 23 of them spin-manifolds, so fermions and a Dirac operator can also be defined on these. Seven of them are appropriate for finite volume periodic boxes undergoing rotation at finite temperature.

We study infrared (IR) divergences from the point of view of permanent pinches. We show how canceling permanent pinches allows us to form finite linear combinations of integrals. We further show how to compute scheme-independent leading IR divergences with- out introducing a regulator, by integrating certain residue forms along desingularizations of permanent pinch varieties. Our methods work for massless and mixed massive-massless inte- grals, for non-planar integrals with arbitrary numerators as well as for integrals with higher (integer) powers of propagators. We use this analysis to determine leading singular terms in some examples of box integrals. We further study examples of finite integrals at higher loops, and in particular provide a basis for finite non-evanescent integrals in a non-planar two-loop five-point topology.

A central challenge in diagnosing quantum chaos is to distinguish genuine many-body scrambling from kinematic effects of the spectrum. Krylov state complexity, or spread complexity, has emerged as a powerful diagnostic, with its characteristic growth, peak, and relaxation often taken as signatures of chaos. However, previous work has shown that this criterion can give false positives: saddle-dominated integrable systems may display prominent peaks even without random-matrix level correlations. We argue, based on complementary numerical and analytical evidence, that this ambiguity can be resolved by unfolding the spectrum prior to constructing the ensuing Krylov dynamics. By removing the non-universal smooth density of states while retaining microscopic spectral correlations, unfolding suppresses spurious peaks in integrable systems while preserving the universal spectral signatures of chaotic systems. Analytically, the formulation of the Lanczos iteration in terms of orthogonal polynomials yields an exact complexity kernel with a robust near-diagonal structure whose fine-grained features reflect the underlying spectral correlations. Moreover, for the logarithmic model, unfolding can be performed exactly, mapping the spectrum to a uniform lattice and yielding an analytic spread complexity that removes the false-positive peak. These findings establish unfolded Krylov complexity as a more reliable probe of genuine many-body scrambling.

We propose quasicrystalline inflation. Six quasiperiodic phases decompose into three phonons and three phasons. It turns out that a coherent pure-phason displacement can generate a local power dipole while the linear traceless quadrupole vanishes. From spatially varying quadratic effective field theory, we derive off-diagonal correlations whose momentum transfer is restricted to integer combinations of the six icosahedral wavevectors. These correlated off-diagonal signals provide a characteristic observational signature of primordial quasiperiodic order, primordial diffraction.

Consider the polynomial $f=x^N+y^N-z^N$ where $x,\,y$ and $z$ are positive integers and $N \ge 3$ is an integer. By Fermat's Last Theorem, $f$ is never zero so that its reciprocal, $1/f$, has no singularities. We therefore study the finite sum of the reciprocal: $S(m,N)=\sum_{x=1}^m\sum_{y=1}^m\sum_{z=1}^{m}\frac{1}{f}$. The terms $1/f$ can be positive, negative and their magnitude is less than unity. A key observation is that $S(m,N)$ can be split into two convenient parts: a dominant contribution $D(m,N)$ that has a simple analytical expression and a remainder $R(m,N)$ which is more complicated but negligible compared to $D(m,N)$. Therefore, $S(m,N)$ is almost identical to $D(m,N)$. The analytical expression for $D(m,N)$ is $(2\,m-1)\,H_m^{(N)}$ where $H_m^{(N)}=\sum_{x=1}^m\frac{1}{x^N}$ approaches quickly the Riemann zeta function $\zeta(N)$ as $m$ increases. Therefore, the original sum $S(m,N)$ has a simple expression: it is basically linear in $m$ with slope equal to $2\,\zeta(N)$. Its linear behavior is not an asymptotic result; plots of $S(m,N)$ vs. $m$ for different $N$ show a straight line starting at $m=1$. $S(m,N)$ deviates slightly from a straight line over a small interval $8\le m\le 12$ for the case $N=3$. This slight deviation is due to Fermat near misses where $x^3+y^3-z^3=\pm 1$ (for $z\ne x$ and $z\ne y$); these create a jump in the remainder $R(m,3)$ at $m=9$. We make a numerical and analytical study of the remainder $R(m,N)$. From the numerical analysis, $R(m,N)$ converges for $N\ge 4$ but it was harder to tell whether $N=3$ converged. An analytical study based on a comparison of $R(m,N)$ to its Cauchy principal value integral, shows that $R(m,3)$ likely diverges logarithmically. It also shows that $R(m,N)$ converges for $N\ge 4$ in agreement with the numerical analysis. We discuss in the conclusion some interesting questions for future investigation.

We investigate whether hairy black holes generated through spontaneous symmetry breaking in Einstein-Scalar-Gauss-Bonnet (ESGB) theory, involving a complex scalar field with a global $U(1)$ symmetry, can be compatible with cosmological evolution. To this end, we introduce the ESGB theory with a scalar self-interaction that becomes relevant on cosmological scales while remaining negligible near the black hole. Owing to the time dependence of the GB term on cosmological scales, the scalar field dynamics in the evolving FLRW background differ qualitatively from those in the nearly static black hole background. In particular, for scalar-GB couplings compatible with hairy black hole formation, the effective potential supports a symmetry-broken vacuum throughout inflation. However, after inflation, a decelerated expansion changes the sign of the GB term, temporarily making the effective potential unbounded from below. As the GB contribution subsequently decreases, the scalar self-interaction eventually dominates and restores the symmetry. Within this schematic framework, we derive stringent constraints on the coupling strengths, the cutoff scale, and the black hole mass, which primarily arise for avoiding efficient tachyonic amplification of the scalar field perturbations during the unbounded phase. For cutoff scales compatible with both cosmological evolution and scalar hair formation, we find that only ultralight black holes with masses of the order of a few grams can develop scalar hair, identifying them as hairy primordial black holes.

The bispectrum of cosmological perturbations is an important probe of inflation and the underlying particle physics. However, calculating it becomes challenging in inflation models where inflaton dynamics is dominated by quantum diffusion rather than slow-roll, especially in the multi-field case. In this paper, employing the stochastic-$\delta \mathcal{N}$ formalism, we propose a Monte Carlo-based method to calculate the bispectrum in the squeezed limit, as an extension of the method for the power spectrum that we previously proposed. Our method involves generating paths of inflatons' time evolution that branch only several times, avoiding nested path generation, which incurs a prohibitive computational cost. As numerical demonstrations, we apply the proposed method to single- and double-field chaotic inflation for validation, and to hybrid inflation with mild waterfall, for which, to the best of our knowledge, the bispectrum is calculated for the first time in this work.

Over the past decade, the bootstrap strategy has transformed the computation of holographic correlators and revealed structures suggesting an emerging scattering amplitude program in AdS. These notes, which are an extended version of the five lectures delivered at the Pre-Strings 2026 School, give a pedagogical introduction and synthesis of these developments. We start with a quick reminder of the essentials of CFT and a brief review of AdS perturbation theory. We then demonstrate in detail the bootstrap strategy for computing holographic correlators in the canonical example 4d $\mathcal{N}=4$ super Yang-Mills theory, at the level of four-point functions and in the regime dual to classical Type IIB supergravity. Several extensions, including higher-point functions, quantum corrections and stringy corrections, are discussed at varying levels of detail. We also explain how the bootstrap strategy can be extended to holographic CFTs with conformal defects, covering a diverse array of different setups.

Effective field theories (EFTs) are a powerful framework for performing high-precision calculations at reduced complexity compared to their fundamental counterparts. A particularly important class of EFTs arises in the non-relativistic (NR) regime. Their construction relies on a different realization of the underlying symmetries, since Lorentz invariance is no longer manifest in covariant form in the NR regime. This behavior imposes a link between certain matching coefficients, and therefore additional constraints, commonly referred to as hidden Lorentz invariance. These constraints are established in quantum field theories on inertial flat spacetime, such as NR quantum electrodynamics. However, deriving these constraints becomes considerably more involved for theories involving physics beyond the Standard Model or formulated in non-inertial spacetime backgrounds, where the hidden symmetry structure is less transparent. In this work, we present an approach to obtain the NR EFT by first constructing a relativistic EFT and then performing a generalized NR reduction based on an extended Foldy-Wouthuysen transformation. We illustrate this method by a quantum chromo-electrodynamics EFT for inertial flat spacetime, describing both electromagnetic and strong interactions, and show how it reduces to the established Lagrangian of NR quantum chromodynamics and electrodynamics. The hidden Lorentz invariance emerges as a direct consequence of the construction. This approach provides a route to obtain the NR limits of more complex theories, \eg Dirac fields in non-inertial spacetime or extensions involving physics beyond the Standard Model. As an example, we apply the method to add the coupling of a pseudoscalar axion field in a simplified model and derive its NR limit.

Effective and thermodynamic derivations of gravity theory in the context of generalized entropy can give rise to multiple, and potentially varying, gravitational couplings, raising the question of which quantity should be identified with the physically measured Newton constant. Motivated by this ambiguity, we formulate the notion of gravitational susceptibility of the horizon. In spacetimes containing multiple horizons, if the entropy is a function on a multi-horizon state space, $S=S(A_1,A_2,\cdots,A_n)$, then the derivatives of the entropy with respect to individual horizon areas define the horizon gravitational response coefficients. Different horizons may possess distinct gravitational responses without requiring multiple fundamental gravitational couplings, analogous to direction-dependent response coefficients in macroscopic media. This framework naturally suggests the possibility that horizon entropies (such as the cosmological apparent horizon and a black hole horizon) can influence one another, which could explain the black hole-cosmology coupled "black hole mass growth" previously discussed in the literature.

We study scalar and electromagnetic perturbations of the root–Kerr object. Its source-free exterior carries the electromagnetic field obtained in the vanishing-mass limit of the Kerr–Newman black hole, while its physical source is a rotating disk with an essential distributional rim contribution. For a massless charged scalar, the minimally coupled Klein–Gordon equation separates into a confluent-Heun (CHE) radial equation with a direct coupling between the scalar and background charges. We give the associated Nekrasov–Shatashvili (NS) dictionary and show that the disk is an ordinary radial point. For electromagnetic pertubations, we derive the equations for the radiative Newman–Penrose Maxwell scalars directly. They have the same confluent-Heun structure, but a Maxwell perturbation has no bulk coupling to the background potential. Charge-dependent photon scattering data therefore cannot be fixed by the exterior equation alone. We formulate the disk/rim boundary-data problem, identify the response data required to convert exact CHE/NS connection coefficients into a physical scattering matrix, and show how all-spin helicity-flip Compton information constrains the response on the radiative subspace. The analysis separates exact exterior propagation and amplitude matching from the additional source dynamics required for a microscopic response.

We set up a truncated numerical approach in the Polyakov bootstrap (PB) framework. We employ a gradient descent optimization to solve PB sum rules numerically, and hence solve crossing for arbitrary deformations of the generalized free field (GFF) spectrum in an iterative way starting from a perturbative solution. For unitary deformations the solutions coincide with extremal CFT spectra. But more interestingly, our findings indicate that a general crossing solution, not necessarily unitary (i.e. without positivity), can be uniquely identified by a smooth connection to GFF. The truncated Polyakov bootstrap approach is established through a number of examples in both single and mixed correlator settings.

Building on Jacobson's thermodynamics derivation of Einstein field equations, the "generalized entropy and varying-G" (GEVAG) framework was proposed to consistently incorporate generalized horizon entropy $S=f(A)/4G$ into both the thermodynamics and the geometry of spacetime. This leads to an effective gravitational coupling $G_\text{eff}=G/f'(A)$. A related "entropy-gravity correspondence" (EGC) instead is equivalent to promoting this horizon relation to a radially varying bulk coupling $G_\text{eff}(r)$. We clarify the similarities and fundamental distinctions between these approaches. Although they share the same horizon consistency relation, their global causal structures and asymptotic geometries can differ substantially. In addition, the radial prescription of EGC introduces an additional ambiguity for multi-center configurations. We further examine a near-horizon extension of GEVAG, which restores the equivalence between thermodynamic and ADM masses that is absent in the horizon-only formulation. We then discuss the implications of these different prescriptions for the Bekenstein bound. The Bekenstein bound provides a surprising link between $G_\text{eff}$ in near horizon GEVAG, EGC, and the one obtained in the recent $f(R)$-reconstruction approach of generalized entropy geometry via Wald entropy. Finally, we raise the most important question: what exactly is the $G$ measured in laboratories?

Dirac leptogenesis offers a qualitatively different route to the baryon asymmetry: total lepton number is conserved, but equal and opposite asymmetries are stored in the Standard Model and right handed neutrino sectors, with only the visible component processed by electroweak sphalerons. We present the first dedicated study of how evaporating primordial black holes (PBHs) modify this mechanism. In a minimal charged-scalar mediator setup, we solve the coupled Boltzmann system including thermal production, Hawking emission of the mediator $X$ and of right handed neutrinos, the PBH contribution to the expansion rate, and entropy injection. We find that Hawking emission can populate $X$ in regions where thermal production is inefficient, allowing its subsequent CP-violating decays to enhance the baryon asymmetry. For representative benchmarks, PBHs extend the successful region from mediator masses around $10^9\,{\rm GeV}$ down to about $10^6\,{\rm GeV}$ and can compensate for smaller effective CP asymmetries. This effect is not universal: where thermal Dirac leptogenesis is already efficient, PBHs can instead reduce the final asymmetry. Their evaporation also deposits energy in the right handed neutrino sector and contributes to $\Delta N_{\rm eff}$. In the PBH parameter scan, part of the region that reproduces the observed baryon asymmetry lies below the Planck reference level $\Delta N_{\rm eff}=0.284$ and above the projected CMB-S4 sensitivity $\Delta N_{\rm eff}=0.06$.

We derive a set of on-shell recursion relations for amplitudes in worldline quantum field theory (WQFT), an effective theory of gravity coupled to a massive worldline which is relevant for computing classical gravitational observables. We overcome the poor large-$z$ falloff of amplitudes under an all-line complex momentum deformation by deriving and exploiting a new soft-graviton theorem in the presence of a worldline. This theorem generalizes the leading (Weinberg) and subleading soft theorems with additional contributions due to soft emission from the worldline. Our main result is a $d$-dimensional recursion formula, expressing any $n$-graviton rational amplitude in terms of lower-point amplitudes from WQFT and pure gravity. Using the soft-worldline theorem, we can obtain amplitudes with any number of external worldline fluctuations from the corresponding all-graviton amplitudes, making the recursion sufficient to construct any rational amplitude of the theory. We verify our results by explicitly computing two-graviton and three-graviton amplitudes.

We derive the one-cycle first Magnusian for nonspinning compact binaries on planar, bound eccentric orbits through relative first post-Newtonian (1PN) order and linear order in radiation reaction, and construct the associated first-order periastron return map. Combining the conservative 1PN dynamics and its Jacobi transport with the 2.5PN and 3.5PN radiation-reaction forces, we obtain all four components in closed form for \(0<e<1\), without expanding in eccentricity. The dependence on all eight Iyer–Will radiation-reaction gauge parameters reduces to periodic coboundaries and therefore cancels over a radial cycle. The result reproduces the averaged energy and angular-momentum losses, their circular limit, and the secular evolution of the 1PN radial orbital elements. The two remaining components encode the dissipative angle-sector information. Projecting the resulting phase-space update onto the perturbed periastron return section yields the corrections to the return time and apsidal phase. We then compare the strict first-order map with a partially exponentiated map built from the same Magnusian. The comparison is observable dependent: at fixed periastron index, the strict map gives smaller residuals for a representative evolution over 40 radial cycles, whereas partial exponentiation reduces the accumulated periastron-timing residual by about an order of magnitude. Across a representative one-cycle grid at equal masses, partial exponentiation improves the radial-action and energy updates at every sampled point.

A discrete, anomaly-free $\mathbb Z_9$ gauge symmetry may persist to the deep infrared, exactly forbidding proton decay. This $\mathbb Z_9$ can emerge from Higgsing a lepton-flavour non-universal $U(1)_X$ that generates realistic neutrino masses and mixings through a high-scale seesaw and predicts an additional light Goldstone. Adding an anomaly-free chiral heavy-quark sector turns this mode into the QCD axion. The same selection rules that ban proton decay also forbid PQ-violating operators below a suitably high dimension, $d_{\rm PQ}\gtrsim10$, including operators involving the heavy quarks that radiatively match onto the scalar potential. We construct explicit models viable when PQ breaking occurs before or after inflation; in the latter case, avoiding stable heavy relics and eliminating the string-wall network tightly constrain the heavy-quark spectrum. We identify restricted regions of parameter space where thermal leptogenesis remains viable and, for $d_{\rm PQ}\geq13$, can coexist with a high-quality axion constituting all of the dark matter.

We construct an algebra of observables associated to a cut of null infinity in asymptotically flat spacetimes. The Bondi mass associated with a sharp cut of future null infinity is not a well-defined quantum operator: its fluctuations diverge even after smearing in retarded time. We instead introduce a finite-radius, time-smeared version of the Bondi mass and adjoin this operator to the matter and graviton observables in an arbitrarily small asymptotic neighborhood of the cut. We separately analyze spacetimes with and without black holes and find, in both cases, Type III$_1$ von Neumann algebras that satisfy non-trivial nesting relations. In Minkowski spacetime, the resulting algebra reconstructs the spacelike wedge associated with the cut. In a stationary black hole spacetime, it reconstructs the region bounded by the cut and the black hole bifurcation surface, providing an asymptotically flat analogue of an entanglement wedge. In the limit as the cut is moved to past infinity, we recover a Type I$_{\infty}$ algebra for spacetimes without black holes and a Type II$_{\infty}$ algebra for black hole spacetimes. For algebras at finite cuts of retarded time, we construct a Type II$_\infty$ regularization of the black hole algebra whose renormalized von Neumann entropy agrees with the generalized entropy. In appendices, we prove two technical results about quantum fields, in a Schwarzschild spacetime, that asymptote to the Minkowski vacuum at infinity: a split property for unbounded, spacelike separated regions and the construction of a faithful, normal, and semifinite Hartle-Hawking weight whose modular flow is Schwarzschild time evolution.

We investigate the geodesic structure and thermodynamics of a $\kappa$-deformed Schwarzschild-anti-de Sitter black hole in a Kiselev quintessence field, where dynamics are governed by a mass-dependent lapse deformation. This term produces an inner Cauchy horizon without requiring charge or spin, yet it fails to resolve the central singularity; instead, the Kretschmann scalar diverges more strongly as $r^{-10}$. Because the deformation amplitude couples to the mass, the standard Bekenstein-Hawking area law violates the first law of thermodynamics. We resolve this by either deriving a modified entropy or rescaling the mass, both of which restore the first law and yield a consistent Smarr relation. Optically, an increasing deformation parameter shrinks both the photon sphere and the critical impact parameter. We also derive a closed-form Joule-Thomson coefficient, revealing that the $\kappa$-deformation triggers an inversion curve a feature absent in standard neutral SAdS. Notably, this occurs without generating a van der Waals critical point, demonstrating that Joule-Thomson inversion and van der Waals criticality can be cleanly decoupled. Finally, the deformation suppresses peak Hawking emission by a factor of roughly four and increases flux sparsity, an effect driven almost entirely by a drop in temperature rather than changes to the black hole shadow.

We propose Higgsino dark matter as a potential interpretation of the $248~\mathrm{keV}$ nuclear-recoil event of interest reported by the LUX-ZEPLIN (LZ) experiment. LZ studied several rare background processes and detector effects in detail, but did not identify any as a likely explanation of the event. A nearly pure Higgsino naturally realizes inelastic dark matter through the off-diagonal $Z$ coupling of two nearly degenerate neutral Majorana states separated by a mass splitting $\delta$. The same electroweak interaction fixes the inelastic Higgsino-nucleon scattering cross section, rather than leaving it as a free parameter. We show that the predicted Higgsino inelastic scattering cross section approaches the published LZ two-sided 90% confidence interval for a Higgsino mass $m_{\widetilde H}\sim1~\mathrm{TeV}$ and a mass splitting $\delta\sim350~\mathrm{keV}$.