Papers

Recent work on metaparticle black-hole thermodynamics suggested the existence of a finite evaporation endpoint characterized by a minimal horizon area, a maximal Hawking temperature, and a stable cold modular remnant. However, the corresponding spacetime geometry remained unknown. In this work we construct an effective geometric realization of the modular remnant within the framework of Born geometry, modular spacetime, and metaparticle dynamics. Starting from a doubled phase-space description in which spacetime coordinates are supplemented by dual coordinates, we derive a Born-doubled Schwarzschild geometry governed by a Born-invariant radial distance. The associated modular uncertainty relation prevents arbitrary localization at the phase-space origin, rendering the classical Schwarzschild singularity physically inaccessible and replacing it with a finite modular core. We then incorporate the metaparticle duality constraint, which induces an effective conformal deformation of the Born-geometric background and generates a nontrivial effective stress-energy tensor. The resulting interior region develops a finite anisotropic source characterized by a tension-dominated radial sector. Localized violations of the radial Null Energy Condition and the Strong Energy Condition arise naturally near the modular core, providing a mechanism through which the focusing assumptions underlying the Hawking–Penrose singularity theorems are evaded. These results establish an effective geometric counterpart of the modular remnant inferred from metaparticle black-hole thermodynamics and suggest that the Schwarzschild singularity is replaced by a finite Born-geometric phase-space structure whose ultraviolet behavior is governed by dual, non-geometric degrees of freedom.

The Ryu-Takayanagi formula equates the area of a minimal surface with the von Neumann entropy of a boundary subregion, and leaves two things about that identification open. The first is how sharply a geometry fixes an entropy. Fannes-Audenaert answers with a Hilbert-space dimension, which diverges as the cutoff is removed however close the two states are. We replace it with the capacity of entanglement, the variance of the modular energy, whose square root grows like the square root of the entangling area where the dimensional factor grows like the regulated volume. The bound is dimension-free and saturated, and it makes the ambiguity of the entropy subextensive for any perturbation whose capacity is small compared with $S_{vN}^2$ times the trace norm. The second is what the area means for a single state, since compression and dilution rates are defined only for many copies while a geometry describes one. When a single replica saddle dominates near $\alpha = 1$, every smooth Rényi entropy at fixed $\alpha > 1$ agrees with $S_{vN}$ to $\textit{O}(\sqrt{S_{vN}})$, as do the smooth min- and max-entropies. The minimal surface therefore fixes every one-shot entropy of the state at once, with large central charge playing the role of large copy number in the asymptotic equipartition property. As a consequence we bound how far outside the holographic entropy cone a holographic state can appear to fall, leaving estimation and certification open.

In this work, we introduce a vortex-impurity model that admits BPS configurations containing both vortices and antivortices and allows vortex-antivortex annihilation to be described within the moduli-space approximation. For a suitable class of impurities, the BPS equations can be mapped through a coordinate transformation onto those of the impurity-free Abelian-Higgs model. In particular, we identify nonlocalized impurities that act as mirrors, generating a vortex-antivortex pair symmetrically placed with respect to the impurity. We derive the corresponding moduli-space metric and show that, within the geodesic approximation, the pair approaches the annihilation configuration asymptotically. We further extend the construction to chains and two-dimensional arrays of alternating vortices and antivortices. Finally, we introduce radial bump impurities that produce stretched and compressed vortices with nontrivial internal magnetic structures.

We show how amplitudes from the scattering of gravitational waves off compact objects in worldline effective field theory can be efficiently computed to arbitrary order in Newton's constant $G$. Our approach solves an effective wave equation for the partial-wave amplitude in which Wilson coefficients (tidal Love numbers) enter through boundary conditions at short distances. We then perform the sum over partial waves to obtain the momentum-space Compton amplitude in terms of elliptic polylogarithms. We reproduce recent results through $\mathcal{O}(G^4)$ and obtain new predictions up to $\mathcal{O}(G^7)$, with Love numbers first contributing at $\mathcal{O}(G^5)$. We find the first ultraviolet divergence in a classical gravitational amplitude at $\mathcal{O}(G^7)$, showing that a pure point-particle description is not consistent in general relativity. Matching to black hole perturbation theory, we show that static Love numbers vanish on-shell and predict subleading non-zero Schwarzschild black hole Love numbers.

We draw on 't Hooft's seminal formulation of the holographic principle to analyse the methodological and conceptual role of information in quantum gravity. We argue that, in 't Hooft's work and in later developments, information functions as a substantive guiding principle. We distinguish three aspects of this role: First, holographic bounds on the amount of information that can be stored in a region function as theory selection criteria that constrain viable quantum gravity theories. Second, holography functions as a principle of theoretical equivalence: the bulk and boundary theories must describe the same physical content, even though 't Hooft privileges a more fundamental, lower-dimensional, and potentially deterministic boundary description. Third, the distribution and encoding of information connect 't Hooft's proposals to contemporary work on bulk reconstruction, holographic quantum error correction, and ER=EPR, where emergent spacetime structure is tied to patterns of entanglement and redundancy. On the basis of these three roles, we argue that purely epistemic or Shannon-style conceptions of information are inadequate in this context: we instead outline a distinction between what we call maximal and intermediate conceptions that aim to capture the methodological and interpretative roles of information in holographic quantum gravity. We therefore suggest that, in the context of holography and quantum gravity, a more systematic philosophical treatment of the role of information as an interpretation-guiding principle would be desirable.

We develop a nonperturbative, group-theoretic quantization of the effective guiding center theory of a charged particle drifting in a magnetic field in two spatial dimensions, and compare the resulting quantum theory with a corresponding coarse graining of the underlying microscopic theory. In the classical effective theory, the small gyro motion is not resolved, while the motion of the center of the gyro orbit remains observable. The reduced phase space is the physical space itself, so quantization leads to noncommuting spatial coordinates, and the effective theory loses access to the metric structure of physical space, retaining only its area structure. By formulating a prescription to match between the microscopic and effective quantum theories, we find that the predictions of the quantized effective theory are generally consistent with those of the microscopic theory. However, for closed isomagnetic contours the effective theory predicts a quantization of “radius”, a spatial discreteness absent from the microscopic theory. This illustrates that quantization of an effective theory may yield spurious nonperturbative predictions, even if that quantum theory shows no internal signs of breakdown.

Extreme and intermediate mass-ratio inspirals in a dense dark-matter distribution have the effects of the dark matter imprinted on the orbital dynamics of and the emitted gravitational waves from these systems. Prior work has shown that space-based gravitational-wave detectors can measure the dark-matter-induced effects on the gravitational waves, which would give evidence for the presence of dark matter around the massive black hole. In this earlier work, the dark matter has been assumed to have only gravitational interactions (namely, no dark-matter self-annihilation or interactions between dark matter and ordinary baryonic or leptonic matter). In this article, we investigate the gravitational-wave effects of introducing such interactions of dark matter with itself or with ordinary matter in binaries with a neutron-star secondary. We consider broad classes of dark-matter models that change the distribution of dark matter (spikes or annihilation plateaus) and which permit accretion onto the secondary, as well as an increasing or static mass of the neutron star during the inspiral (in addition to the purely gravitational effect of dynamical friction). We find distinctive gravitational-wave signatures of these interactions and of self-annihilation, which in some of the scenarios could be sufficiently large for space-based detectors to distinguish them using gravitational-wave observations of these systems.

The ${\cal M}$-theory dual of thermal QCD-like theories constructed in arXiv:1306.4339, 2004.07259 involves, as shown in arXiv:2211.13186, a closed $G_2$-structure seven-fold $\mathcal{M}_7$ supporting Contact 3-Structures (C3S) that induce a “transverse” $SU(3)$-structure. We prove that this induced structure belongs to the symplectic nearly half-flat (S(nearly)HF) class: $d\omega_\Phi=0$ exactly, while $d\Omega_+$ is suppressed as $\mathcal{O}(e^{-N^{1/3}/\mathcal{O}(1)})$ in the infrared "MQGP limit", leaving $W_\Phi^{SU(3)}=W_2^-$ as the sole non-vanishing Chiossi–Salamon torsion class and completing the $G$-structure classification of the MQGP dual initiated in arXiv:1507.02692,2004.07259, 2211.13186. As a physical application, Kaluza–Klein reduction of the eleven-dimensional Hodge dual of the differential of the $G_2$-structure positive three-form on $\mathcal{M}_7$, organised through the $G_2$/S(nearly)HF torsion data, yields a radial “magnetic field” $\mathcal{B}_{\rm KK}(r)$ whose squared norm factorises exactly into external and internal factors. $\mathcal{B}_{\rm KK}(r)$ satisfies a Bessel-type ODE with a regular singular point at the horizon; normalisability and infrared regularity select $J_2$, with harmonicity of the aforementioned internal factor recovered from the large-$N$ suppression. $\mathcal{B}_{\rm KK}$ is related to the magnetic field of the type~IIA flavour $D6$-branes via a non-linear power law, furnishing a top-down holographic mechanism for generating weak magnetic fields in finite-temperature string theory.

Quantum anomalies strongly constrain the possible behavior of many-body systems. A prime example is the Lieb-Schultz-Mattis (LSM) theorem, which relates UV symmetry and filling constraints to IR features of the energy spectrum and ground-state structure. Here, we ask how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems. Using a spacetime duality, we show that the Liouvillian of a $d$-dimensional repeated quantum channel with a mixed anomaly between strong $S$ and weak $G$ symmetry can be mapped to a $(d{+}1)$-dimensional mixed-state symmetry-protected topological (mSPT) phase. Under this correspondence, the initial and steady states of the channel are identified with boundary states of the higher-dimensional mSPT in the presence of bulk projection. We further introduce the twisted Renyi-$N$ correlator (TRNC) as a probe of temporal correlations in the channel and demonstrate that it is dual to the mSPT strange correlator, providing a direct bulk-boundary route to diagnose long-range temporal order implied by the LSM anomaly. Finally, we identify the Liouvillian singular spectrum, rather than the Liouvillian spectrum itself, as a more fundamental diagnostic of quantum anomalies, and show that it is dual to the operator entanglement spectrum of the mSPT.

We study overlaps of late-time states in semiclassical de Sitter quantum gravity. In a family of deformations of de Sitter JT gravity, we compute the no-boundary wavefunction to one-loop and derive the ultralocal late-time measure. The one-universe contribution to the norm is exactly eight times the sphere amplitude, so the pairing used by the Lorentzian measure differs from that implicit in Euclidean gravity. After summing over disconnected final universes, the no-boundary norm exponentiates the one-universe result, giving $\langle \!\langle \text{HH}|\text{HH}\rangle\!\rangle \approx \exp(4Z_{\rm sphere})$ rather than the sum over closed geometries, $Z_{\rm closed}\approx \exp(Z_{\rm sphere})$. We also review an analogous mismatch in Einstein gravity with positive cosmological constant, where the late-time no-boundary norm vanishes at one-loop, differing from the Euclidean sphere amplitude. We discuss the implications for cutting and gluing in perturbative gravity, and features that arise when extending this construction to sums over topologies.

We establish the spectral foundation of the geometric formulation of Cooper pairing in the Yukawa–Sachdev–Ye–Kitaev model. Starting from the large-$N$ bilocal effective action, we derive the Gaussian fluctuation kernel in the even-frequency spin-singlet Cooper channel. Following the construction of Maldacena and Stanford, we determine the kernel eigenvalue $k\left(h\right)$ analytically for arbitrary conformal weight $h$ and resolve the pairing fluctuations into the continuous and discrete sectors of the associated de-Sitter space Laplacian. We show that the superconducting instability and the universal low-energy fluctuations near it reside entirely in the continuous scattering sector, while the discrete modes remain non-critical. Expanding the kernel about the lowest continuum mode yields a Klein–Gordon action on ${\rm dS}_2$, restricted to the continuous spectral subspace. This is precisely the subspace on which the inverse Radon transform to ${\rm AdS}_2$ is well defined. The projected bilocal Cooper-pair field can therefore be mapped onto a scalar matter field propagating in ${\rm AdS}_2$, without requiring any further spectral restriction on the bulk theory. Our results provide the missing microscopic justification for the projection implicit in earlier holographic formulations and clarify how a local bulk field emerges from the bilocal pairing theory.

Energy correlators are universal observables, well defined across a wide range of theories and spacetime dimensions, from gauge theory and conformal field theory to string theory. Energy correlators are constrained by three fundamental properties: pointwise positivity of the energy flux, global positivity originating from their interpretation as state norms in a unitary theory, and energy conservation organizing multi-point energy correlators into an infinite consistent hierarchy. We argue that the most general solution to the infinite hierarchy positivity problem of energy correlators is given by the event distribution formula, which expresses energy correlators as moments of the measure on the space of probability measures on the celestial sphere. We work out in detail implications of positivity for two- and three-point energy correlators and show that it implies nontrivial two-sided bounds on their multipole expansion coefficients. The bounds obtained by requiring consistency of the infinite hierarchy of energy correlators are strictly stronger than those obtained by imposing positivity of the two- and three-point correlators alone. For the low-spin multipole coefficients studied in the paper, the derived bounds are optimal in the sense that their extrema are realized by finite mixtures of finite-particle events. We further demonstrate consequences of positivity in energy correlators in collider physics and conformal field theories.

Motivated by inflation and Liouville theory, we consider random $d$-dimensional geometries characterized by an overall scale factor $ds^2 = e^{2 \zeta} dx^2 $ given in terms of a random Gaussian field $\zeta(x)$ with logarithmic correlations. We discuss aspects of the renormalization of the volume element $e^{d \zeta }$, connecting well-known Liouville theory formulas (KPZ) and inflationary ones. By starting from a fixed physical cutoff and coarse-graining operators to a fixed fiducial cutoff, defined via the flat metric $dx^2$, we provide a direct physical derivation of the KPZ scaling relation. We point out that the same renormalization problem arises in stochastic inflation, where it is modeled by Brownian motion of the inflaton field. We show that the breakdown of the renormalization of the Liouville volume when the fluctuation amplitude exceeds a critical value corresponds to the transition to eternal inflation. In $d = 2$, this matches the familiar $c_m = 1$ barrier in Liouville gravity. We also discuss connections to mathematical probabilistic approaches to random surfaces.

Self-dual Einstein gravity is a one-loop exact, UV and IR finite, diffeomorphism invariant, non-unitary theory of quantum gravity in four dimensions. The only non-trivial amplitudes are the one-loop-all-plus amplitudes, and they are equal to those of pure Einstein gravity. In these notes we review SDG and SDYM pedagogically. We walk the reader through key calculations, fill in some gaps in the literature, and point out directions for future research. Topics include: derivation of the self-dual actions from the full Einstein gravity/YM actions in lightcone gauge, decoupling of ghosts, Berends-Giele currents, vanishing of tree-level-one-minus amplitudes, celestial $Lw_{1+\infty}$ symmetry, perturbiners, double-off-shell current calculation of one-loop-all-plus SDYM and SDG amplitudes, dimension shifting, unitarity cuts, the BDPR gravity formula, one-loop color ordering, and the covariant formulations of the self-dual theories as well as their their gauge fixing. We also review some selected results from the celestial holography program, and briefly comment on an all-n expression for the one-loop-one-minus gravity amplitudes.

We investigate the problem of confinement of massive ghost, which violates the unitarity of the physical S-matrix, in quadratic gravity on the basis of a manifestly covariant and local canonical operator formalism. First, we reconsider the manifestly covariant quantization of quadratic gravity in the de Donder gauge (the harmonic gauge) from the viewpoint of dipole fields. Next, we also reconsider a possible mechanism of confinement of the massive ghost and derive an effective Lagrangian for asymptotic fields of a BRST quartet where the asymptotic field corresponding to the massive ghost is found to obey a dipole field equation as in the Froissart model, which is a characteristic feature in our formalism. To understand quantum aspects of our theory, we perform a manifestly covariant quantization of the effective Lagrangian in two different ways based on the three-dimensional Fourier transform and the four-dimensional Fourier transform, and derive the same result that the quantum Fock space is spanned by multipole states.

In this note, we describe the Gepner construction purely as orbifold (rather than a beta-prescription or orbifold-like process). This is done by distinguishing orbifolding by a chiral symmetry from that by a left-right diagonal symmetry, and also by exploiting an extra degree of freedom available in orbifolds of Type 0 SCFTs. We also describe by using the Arf theory how the extra freedom in Type 0 SCFT orbifolds in general (not just in the Gepner construction) should be implemented in higher genus amplitudes. This note also determines when a combinatorial data set of a Gepner construction has a mirror Gepner construction, and also provides two thinking frameworks to determine the SCFT vertex operators of the Gepner model SCFTs with phase ambiguity and branch cuts under control.

$X$ is a Nakajima quiver variety. In this note we report the observation that the space parameterizing quasimaps from $\mathbb{P}^1$ to $X$, sending infinity to a given point, may be presented globally as the critical locus of an explicit function.

We investigate the cosmological evolution of a universe with an initially large negative vacuum energy, corresponding to an anti-de Sitter (AdS) space-time. Such a universe inevitably contracts and collapses into a singularity. To prevent this collapse, we propose a dynamical mechanism of vacuum energy compensation based on a scalar field non-minimally coupled to the curvature scalar. Numerical and analytical calculations demonstrate that the suggested mechanism completely compensates the gravitational impact of the vacuum energy, successfully driving the curvature to zero. As a result, the universe avoids the singularity and evolves into a power-law expansion, typical for a radiation-dominated cosmology.

The predicted extent of inhomogeneous chiral phases in effective models of quantum chromodynamics is notoriously sensitive to ultraviolet regularization. We show that this sensitivity is largely artificial. In the two-flavor Nambu–Jona-Lasinio model, conventional implementations of three-dimensional cutoff, Pauli–Villars, and proper-time regularization produce strongly different finite-momentum instability regions. Once ultraviolet regulators are restricted to genuinely divergent vacuum contributions, however, all three prescriptions yield nearly identical stability diagrams. Both the onset of the moat regime and the subsequent finite-momentum instability become quantitatively robust. The apparent scheme dependence originates from regulating ultraviolet-finite medium contributions associated with the Fermi-surface response. Our results identify spatially modulated chiral correlations as a genuine property of the dense medium rather than an artifact of the ultraviolet prescription.

Starting from the identity $e^{2\pi i J_z}=(-1)^{F}=e^{i\pi Q}$ on the color-singlet physical state space, we derive a density-operator identity that ties imaginary rotation to an imaginary quark chemical potential, $\rho(\Omega_I+2\pi,\theta_q)=\rho(\Omega_I,\theta_q+\pi)$. Hence imaginarily rotating $SU(3)$ QCD at $(\Omega_I,\theta_q)=(2\pi,0)$ is mapped exactly onto the Roberge-Weiss (RW) point $(0,\pi)$, where charge conjugation $C$ is spontaneously broken above the RW endpoint—a conclusion independent of any model or approximation. Minimizing the one-loop effective potential on the rotation axis, we obtain analytically, for three massless flavors, the second-order transition at $\Omega_{I,C}/\pi=(22-2\sqrt{22})/9$, and a subsequent first-order transition at $\Omega_{I,{\rm lock}}/\pi=2/3+2\sqrt{111}/27$. At smaller $\Omega_I$, a continuous degeneracy of the massless one-loop approximation leaves the realization of $C$ undecided; a finite strange-quark mass lifts it. We also state how the exact relations and the on-axis predictions can be tested in lattice QCD.

Motivated by the kinematic-space description of gravitational subregions \cite{Basu:2026hbg}, we allow partial entanglement entropy (PEE) threads to be sourced not only from the asymptotic boundary, but also from boundaries of subregions. Based on this setup, we develop a framework to construct configurations for PEE threads and bit threads sourced from surfaces in the AdS bulk. The situations we have analyzed include the Poincaré AdS$_3$ and the planar BTZ black brane with an end-of-the-world (EOW) brane, and the entanglement wedges of boundary multi-intervals. We construct novel configurations of PEE threads and bit threads in these situations, which shed new light in our understanding of the AdS$_3$/BCFT$_2$ correspondence and the holography defined in the entanglement wedge motivated by surface/state correspondence. A notable feature we found is that, although the elementary PEE threads are geodesics, the integral curves of the coarse-grained bit-thread current are generically not geodesics. Across the explicit constructions, the integrated source currents reduce to endpoint distance-difference potentials, which make divergencelessness, the norm bound and bottleneck saturation geometrically transparent. Our results clarify how boundary, brane, horizon and RT-surface degrees of freedom participate in holographic entanglement and provide a concrete link between PEE, bit threads, subregion kinematic space and the surface/state correspondence.

We develop PEE thread flows for the planar BTZ black brane and finite-cutoff holography. Exact geodesic-distance kernels define source-resolved PEE thread currents whose superposition gives divergenceless bit-thread fields. In BTZ, boundary-boundary and boundary-horizon sectors reproduce the entanglement contour and thermal horizon flux. At finite cutoff, the two-point PEE kernels are smooth and select macroscopic flows that are generically non-geodesic despite being built from geodesic elementary threads. We compare these PEE-selected flows with independent normal-geodesic bit-thread flows and show that they saturate the same RT bottleneck while differing in boundary calibration, endpoint pairing and off-bottleneck structure. The resulting constructions make explicit both the endpoint organization of finite-cutoff entanglement and the nonuniqueness of holographic max flows.

Generalized horizon entropies are widely used as theoretical modifications of the Bekenstein-Hawking area law, but through the Wald construction they may also encode modifications of the underlying gravitational dynamics. We reconstruct metric $f(R)$ gravity from prescribed entropy-area relations and show that the procedure is intrinsically branch dependent through the required area-curvature map. On the maximally symmetric branch, where $A=48\pi/R$ exactly, the reconstruction reduces to a single quadrature and can be performed non-perturbatively. We obtain closed-form Lagrangians for several generalized entropies and show that an entropy term $a~S_{BH}^{q}$ generates a curvature term proportional to $R^{2-q}$. In particular, Kaniadakis entropy produces a $1/R$ correction, while logarithmic entropy generates an $R^2\ln R$ term. We further derive a branch-independent criterion, $\partial_{R}^{2} f=(ds/dR)d(S/s)/ds$, relating Dolgov-Kawasaki stability directly to the entropy functional, together with $m_{\rm sc}^2=S'(s)/(3f_{RR})$ on the maximally symmetric branch. Comparison with the fixed-mass Schwarzschild-de Sitter branch reveals different reconstructed Lagrangians and reversed stability properties. Finally, the weak-isolated-horizon boost charge reproduces the original generalized entropy. These results establish a direct non-perturbative link between generalized horizon thermodynamics and modified gravitational dynamics.

We examine possible $C$-odd effects in elastic proton-proton and proton-antiproton scattering in the diffractive dip region. Collider data with $\sqrt{s}>500$ GeV are fitted for $0.2<|t|<1~\GeV^2$, using a simple Regge-inspired parametrization of effective $C$-even and $C$-odd amplitudes. The relative phases are not left free, but are fixed by the signature factors of the corresponding even and odd contributions. In this way, the real and imaginary parts of each term are linked by crossing. The $C$-even amplitude is first described by three effective Pomeron-like terms. The $C$-odd sector is then tested with several one-term Odderon-like forms. We find that the fits do not require a stable nonzero $C$-odd term: the odd contribution is either compatible with zero or becomes weakly constrained when we allow extra freedom. We then test whether the conclusion is changed by adding either a fourth Pomeron-like term or a second Odderon-like term. The improvement obtained with the fourth Pomeron-like term is mainly $C$-even, while the second Odderon-like term is not resolved as an independent contribution. These results provide a complementary test of recent determinations of the Odderon amplitude based on scaling and analyticity.

We study pair creation for quantum fields of spin $0$, $1/2$, and $1$ in the presence of weak gravitational and gauge backgrounds. Using resummed heat-kernel techniques, we obtain closed expressions for the pair creation probability up to quadratic order in the “generalized curvatures”. In addition, for gravitational backgrounds, we recast the pair production probability in terms of the matter distribution required for consistency with the Einstein equation. Finally, to illustrate the powerfulness of our methods, we analyze the effect of pair creation in a binary star system.

We present a leading-order study of the rare exclusive decays $t \to bM$, where $M$ denotes a pseudoscalar or vector meson. Starting from the tree-level transition $t \to bW^* \to b(q\bar q')$ and using a factorization approximation, we derive compact expressions for the amplitudes and partial widths in which the long-distance QCD dynamics is encoded in the meson decay constants $f_M$. We provide numerical branching-ratio predictions for representative modes such as $t \to b\pi^+$, $t \to bK^+$, $t \to bD_s^{(*)}$, and $t \to bB_c^{(*)}$, finding $\mathrm{Br} \sim 10^{-8}$–$10^{-7}$. For vector final states, we derive helicity amplitudes and Standard-Model polarization fractions, and we outline the sensitivity of these observables to anomalous chiral $tWb$ couplings in the limit $m_b \to 0$. Our results provide an updated Standard Model (SM) baseline for rare exclusive top-quark decays and a starting point for EFT interpretations of non-standard charged-current interactions.

We first construct general saddles of the five-dimensional gravitational supersymmetric index with $S^1\times\mathbb{R}^4$ asymptotics, carrying an arbitrary number of electric charges and Gibbons-Hawking centers. We then uplift the three-charge configurations to type IIB supergravity, obtaining solutions asymptotic to $S^1\times \mathbb{R}^4\times S^1\times {\rm K}3$, carrying D1-D5-P charges. Upon taking a decoupling limit, these solutions yield asymptotically Euclidean AdS$_3\times S^3\times {\rm K}3$ candidate saddles of the dual CFT$_2$ elliptic genus. We focus on the two-center saddles, which involve three integers specifying an orbifold action. Depending on these integers, the saddles may or may not possess a Euclidean horizon, and may be smooth or exhibit orbifold singularities. We give the on-shell action of these two-center saddles in the appropriate ensemble and establish a precise match with the Farey-tail expansion of the elliptic genus. The horizonless saddles are the Euclidean version of fractional spectral-flow solutions previously discussed in the literature, corresponding to $({\rm AdS}_3\times S^3)/\mathbb{Z}_k$ orbifolds. The black hole saddles are modular images of the horizonless ones. They generalize the well-known ${\rm SL}(2,\mathbb{Z})$ family of BTZ black holes by placing it in the background of the $\mathbb{Z}_k$ orbifold. We also consider the asymptotically AdS$_3\times S^3$ solutions arising as decoupling limit of five-dimensional black ring and black lens saddles, provide their on-shell action and confirm that they do not contribute to the D1-D5 elliptic genus.

Ultralight bosonic fields can form macroscopic clouds around rotating black holes, whereas the existence of analogous stationary fermionic condensates is strictly constrained by their intrinsic spin. Here we establish a complete geometric and kinematic framework to resolve the stationary bound states of massive Dirac fields on Kerr and Kerr-Newman backgrounds. By mapping the Kerr-Dirac system to a globally integrated sourced radial problem, we strictly isolate the boundary constraints dictated by horizon causality. The angular sector reveals a fundamental topological distinction: because the azimuthal quantum number is strictly half-integer, the regular boundary branches prevent the local field density from vanishing on the rotation axis. Consequently, rotating fermionic clouds inherently form globally filled, oblate geometries, in stark contrast to the hollow toroidal structures characteristic of scalar condensates. Crucially, our radial indicial analysis unveils the exact mathematical origin of the absence of synchronized Dirac hair. Precisely at the kinematic synchronization locus, the Frobenius matrix of the Dirac operator is non-defective and entirely devoid of logarithmic divergences. Without these singular branches to be selectively excised by boundary regularity, the physical burden of existence falls entirely onto the causal flux barrier, which strictly trivializes the zero-source amplitude. This synchronization veto demonstrates that a black hole's capacity to support macroscopic stationary fields is governed not merely by superradiant kinematics, but by the profound interplay between local horizon causality and quantum spin statistics.

The blowup equations of Huang, Sun and Wang are bilinear relations satisfied by the refined topological string partition function of a local Calabi–Yau 3-fold. We prove the blowup equations for the local Hirzebruch surfaces \(\operatorname{Tot}_{\mathbb F_\ell}K_{\mathbb F_\ell}\), \(0\leq\ell\leq2\), as identities of torus-equivariant symmetrized \(K\)-theoretic stable pair invariants; for \(\ell=2\) the invariants are localized indices. The proof identifies the stable pair vertex sum, after division by the fibre contribution, with the equivariant Euler characteristic of \((\det\mathcal V)^\ell\) on the moduli space of framed rank \(2\) sheaves on \(\mathbb P^2\). The blowup formulas of Nakajima–Yoshioka for framed sheaves then yield the unity and vanishing equations. For local \(\mathbb P^2\) we obtain the blowup equations conditionally on two explicitly stated conjectures. We also state the Huang–Sun–Wang conjecture for general local Calabi–Yau 3-folds in the language of stable pairs, and formulate stable pair conjectures for the local rational elliptic surface involving the \(E_8\) lattice.

We consider a class of three-parameter metrics that was introduced in \cite{azizallahi2024three}. The class of metrics contain Zipoy-Voorhees (ZV) and Fisher-Janis-Newman- Winicour (FJNW) spacetimes at certain values of the parameters. We build an axially symmetric and asymptotically flat spacetime with gravitomagnetic effects by introducing a Newman- Unti-Tamburino (NUT) charge into this class of metrics via the Ehlers transformation. We investigate the physical features of this class of Taub-NUT-scalar (TNS) metrics including gravitational lensing, quasinormal mode (QNM) spectra, and test particle motion. Our results provide fresh insight on how mass, multipole moments, and gravitomagnetic fields behave in the presence of a scalar field and show the effect of the NUT charge on stability of orbits in this class of metrics.