Papers

Classical black holes have sharply defined event horizons, but quantum mechanically the horizon acquires a quantum uncertainty, called the `quantum width' by Marolf. We propose a definition of the quantum width by a physical experiment involving the last moment a signal emitted from an ingoing light ray can escape to infinity. Calculations of this observable for spherically symmetric black holes in perturbative quantum gravity reveal that the quantum width depends on the resolution of the probe, and is often much larger than the Planck scale. For example, for Schwarzschild black holes in four dimensions in a particular regime of parameters, a piece of the horizon of size $\sigma_\perp$ has quantum width roughly $\sqrt{l_P r_s^2/\sigma_\perp}$.

We compute the classical gravitational Compton amplitude at the fourth post-Minkowskian order, $\mathcal{O}(G^4)$, within the Worldline Quantum Field Theory framework. We derive the associated $N$-matrix element, which provides the gravitational-wave scattering phase shift at the same order. As a nontrivial check, we show that our result agrees with black-hole perturbation theory.

We construct a new class of exact solutions describing multi-black holes in the Bertotti–Robinson spacetime, using the monodromy-matrix formalism associated with integrable sigma models. Starting from the extremal Reissner–Nordström black hole in the Bertotti–Robinson background, we derive the corresponding coset and monodromy matrices and show that they are governed by nilpotent algebraic structures. This property enables an explicit factorization of the monodromy matrix, allowing for a systematic reconstruction of the underlying gravitational solutions. We extend this construction to multi-center configurations by introducing multiple poles in the monodromy matrix, leading to Majumdar–Papapetrou–type solutions with Bertotti–Robinson asymptotics. Each center is shown to correspond to a regular extremal black hole with an $\mathrm{AdS}_2 \times S^2$ near-horizon geometry, and the asymptotic end likewise approaches a Bertotti–Robinson geometry. We further generalize the framework to stationary configurations in the Bertotti–Robinson spacetime, as well as to a broader class of Israel–Wilson–Perjés-type solutions, by considering more general nilpotent elements. Our results demonstrate that the monodromy-matrix approach provides a powerful and systematic framework for constructing multi-black hole solutions in nontrivial backgrounds, and suggest a promising route toward more general configurations.

We show that Abelian and nonabelian gauge transformations are the analog of $W_\infty$ transformations for higher dimensional quantum Hall effect. The commutator anomaly and the extended algebra of such transformations on the edge modes of a droplet are obtained by purely topological arguments, basically utilizing the two-cocycle in the descent procedure for anomalies and using the fact that there is anomaly cancellation between the bulk and boundary actions. The method relies on the fact that bulk actions are easily constructed in general using the Dolbeault index theorem. The resulting algebras are shown to agree with explicit edge mode calculations for cases where they are available. We also comment on the similarities and differences in the nature of these transformations between two and higher dimensions.

We investigate the analytic structure of the quark propagator in the Landau gauge by dynamically coupling the standard gap equation to the non-perturbative quark-gluon vertex. Employing the full vertex basis, we demonstrate that for sub-GeV time-like momenta, the proper inclusion of the underlying dynamics leads to a pair of real poles with opposite-sign residues. In particular, in stark contradistinction to the results obtained in widely used approximations, we see no sign of complex conjugate poles. This distinctive analytic structure evades conceptual shortcomings frequently associated with complex conjugate poles while remaining fully compatible with the aspects of color confinement related to positivity violation. Crucially, this novel behavior is governed by a dominant triplet of vertex form factors: the tree-level component, the anomalous chromomagnetic moment, and a component we label as "spin-momentum curvature". By gradually tuning the individual strengths of these components, we demonstrate that while they contribute in distinct ways to the quark propagator, their joint action is vital for stabilizing the system. Together, they place the low-lying poles onto the real axis while producing a robust constituent quark mass of $350$ MeV.

Non-linear dRGT massive and bimetric gravities are complicated theories constructed in terms of square roots of matrices. Apart from the technical issues of successfully working with such square roots, there is also a problem of their non-uniqueness. There are claims in the literature that one should better use the principal root. This is a very reasonable conclusion. However, the motivation they give for it is that otherwise there would be non-primary square roots violating the general covariance. In this paper, I would like to show that, if properly understood, the non-primary square roots are also perfectly covariant. At the same time, I recall the relatively old observation that the real problem with such square roots lies in perturbation theory around them. In terms of matrices, it simply does not exist. In terms of the elementary symmetric polynomials used in the Lagrangian density, it is not analytic. Moreover, the non-principal square roots are more prone to getting into the complex domain.

We bootstrap quantum anomalies using on-shell techniques in the simplest setting: at three points. The necessary field-theoretic input includes the local or global classical symmetry, which the anomaly may break, and the symmetries of the effective action — though not its explicit form. We use massless helicity spinors together with an on-shell representation of the discrete C, P, and T transformations. Our approach determines the Weyl, chiral (global and local), diffeomorphism, and Lorentz anomalies up to real constant prefactors and terms that vanish on shell. In particular, we recover gauge-anomaly cancellation conditions, as well as find that the Weyl anomaly should not involve Pontryagin densities.

Bayesian inference of the neutron star (NS) equation of state (EOS) generally assumes that improved observations primarily reduce posterior uncertainties while leaving inferred EOS parameters unchanged. Using mock measurements of the radius of a canonical $1.4\,M_\odot$ NS with identical central values but varying observational precisions, we show that the inferred posterior means of EOS parameters can shift systematically as the measurement uncertainty changes. We demonstrate that this behavior originates from previously unidentified nearly universal inverse mappings between the NS radius $R_{1.4}$ and empirical EOS parameters. Across a broad range of observational precisions, posterior samples collapse onto nearly unique functions. These mappings are largely independent of observational precision and define a low-dimensional EOS manifold underlying Bayesian inference. We show that the precision dependence of inferred EOS parameters arises from nonlinear filtering of the posterior radius distribution through these mappings. In the narrow-distribution limit this effect reduces to a Jensen-type correction proportional to the local curvature of the inverse mapping, while for presently realistic uncertainties the full nonlinear-filtering relation accurately reproduces the posterior means. Our results reveal a geometric origin of precision-dependent inference in NS EOS studies and provide a new framework for connecting astrophysical observations directly to microscopic nuclear many-body theories.

Spectral densities link experimental measurements to dynamical properties of a quantum field theory which, in turn, can be resolved non-perturbatively from the Euclidean time-dependence of correlation functions. By making extensive use of integral transforms, we present analytic formulae to carry out the inverse Laplace transform so as to extract spectral densities from either the continuum or the discrete sampling of correlation functions in the Euclidean time. Formulae extend to regulated and/or smeared spectral densities as well. We explicitly show that the proposed lattice solution tends to its continuum counterpart up to $O(a^2)$ effects in the lattice spacing $a$ if the lattice correlator is $O(a)$-improved. In practical computations, lattices have necessarily a finite Euclidean temporal extent, a lack of knowledge which suggests to introduce incomplete integral transforms and the corresponding incomplete smeared spectral densities. The contribution from the unknowns to a smeared spectral density can then be rigorously bound and kept under control if the integral transform of the smearing function decays fast enough with the conjugate variable. Conversely, the bound can be used to plan lattices so as to achieve a given target precision on the reconstructed spectral density of interest. The formulae presented here in the context of lattice field theory can be easily applied or extended to other areas of research.

We study the quantum fluctuations of the black hole horizon in three-dimensional Anti-de Sitter (AdS) spacetime. We define a precise protocol to calculate the horizon fluctuations and define a corresponding “quantum width” of the horizon. We relate the horizon fluctuations to boundary correlation functions via holography. Working in perturbative quantum gravity, we find that the quantum width is typically of order $(G_\mathrm{N} L_{\mathrm{AdS}}^3 )^{1/4}$, which is parametrically larger than the Planck scale. In detail, the quantum width depends on the scale at which it is measured, diverging logarithmically in the UV. Our results give the most rigorous evidence to date of gauge-invariant fluctuations at scales much larger than the Planck scale within perturbative quantum gravity.

We investigate the configurational temperature estimator in interacting matrix models and Gaussian random-matrix ensembles. The estimator follows from an exact Schwinger–Dyson identity and may be expressed in terms of the gradient and Hessian of the action. We study the Gross–Witten–Wadia model, a quartic double-well matrix model, and the Gaussian Orthogonal, Unitary, and Symplectic Ensembles. In all cases, the estimator satisfies the exact Schwinger–Dyson identity, $\beta_{\rm config} = 1$, within statistical uncertainties. Separating the estimator into isotropic and anisotropic parts, we find that the leading finite-$N$ corrections satisfy the approximate relation $\beta_{\rm iso} - 1 \simeq - \beta_{\rm aniso}$. We also show that the configurational temperature estimator provides a sensitive diagnostic of Monte Carlo simulations.

The QED scattering amplitude in a chiral medium characterized by a constant chiral chemical potential $\mu_5$ and chiral magnetic conductivity $b_0$ is analyzed. We show the emergence of the resonant behavior in $1\to 2$, $2\to 2$, and $2\to 3$ processes. We compute the rates of paradigm $1\to 2$ processes that determine the widths of quasi-stationary fermion and photon states in the medium. We elucidate the origin of these resonances, the conditions of their emergence, and the physical principles of their regularization.

We present a comprehensive review of regularization schemes for magnetized dense quark matter within effective models of quantum chromodynamics, focusing on the Magnetic-Field-Independent Regularization (MFIR) and the Medium Separation Scheme (MSS) at finite chemical potential and magnetic field. In nonrenormalizable frameworks such as the Nambu-Jona-Lasinio model, the treatment of ultraviolet divergences is crucial, particularly in magnetized and dense environments where conventional regularization procedures may introduce unphysical artifacts. We show that MFIR consistently isolates divergent vacuum contributions from finite magnetic-field-dependent terms, while MSS extends this separation to the medium sector, ensuring that only vacuum quantities are regularized. Within this unified framework, we analyze the thermodynamics of cold and dense quark matter, including color-superconducting phases, and demonstrate that the superconducting gap remains finite at large chemical potentials, even in the presence of strong magnetic fields. In contrast to results obtained with traditional regularization schemes, we find no evidence for a transition to a normal phase at zero temperature, highlighting the importance of a proper separation between vacuum and medium contributions. These results eliminate spurious oscillations and other nonphysical artifacts, leading to a more robust and physically consistent description of strongly interacting matter under extreme conditions relevant to compact stars and heavy-ion collisions.

We present a systematic procedure for constructing brane brick models corresponding to abelian orbifolds of toric Calabi-Yau 4-folds, extending the orbifold construction beyond the well-studied case of abelian orbifolds of C^4. Given a parent brane brick model corresponding to a toric Calabi-Yau 4-fold M, we show that the action of an abelian orbifold group Gamma on the generators of M induces an action on the chiral and Fermi fields as well as the J- and E-terms of the associated 2d (0,2) supersymmetric gauge theory. The requirement that the orbifolded brane brick model remains consistent with the closed paths associated with the J- and E-terms, together with the chiral cycles formed by their products, precisely reproduces the Calabi-Yau condition on the orbifold action. This procedure yields an explicit formula for the J- and E-terms of the orbifolded brane brick model in terms of those of the parent theory. We apply our construction to the brane brick models corresponding to Q^{1,1,1} and D_3, and present the resulting families of 2d (0,2) quiver gauge theories. We also present explicit expressions for generating functions that count distinct abelian orbifolds of Q^{1,1,1} and D_3.

We present a first-principles lattice-QCD determination of Mellin moments of the unpolarized pion and kaon parton distribution functions using matrix elements of boosted mesons coupled to nonlocal operators containing a straight Wilson line. The calculation is performed on an $N_f=2+1+1$ ensemble of maximally twisted-mass fermions with a clover term, with lattice volume $32^3\times64$, lattice spacing $a=0.0934$ fm, and pion mass $m_\pi=260$ MeV. Matrix elements are computed for hadron momenta $P_3=0$, 0.41, 0.83, 1.25, 1.66, and 2.07 GeV and analyzed within the short-distance factorization framework. We investigate the dependence of the extracted moments on the truncation of the operator-product expansion, the coordinate-space fit window, and the perturbative accuracy of the Wilson coefficients, comparing next-to-leading-order and next-to-next-to-leading-order results. We also perform an RG-improved analysis as a consistency check of the perturbative treatment. Our final results are obtained from combined fits in $(P_3,z)$ space at next-to-next-to-leading-order and are quoted at $\mu=2$ GeV. We also study the SU(3) symmetry-breaking effect and reconstruct the valence PDFs from the moments.

We investigate the phase transition of Quantum Chromodynamics (QCD) with three degenerate quark flavors at zero baryon chemical potential. Using Möbius domain-wall fermions as the lattice fermion formulation, we ensure excellent chiral symmetry preservation. Our simulations are performed at three different temporal lattice extents, $N_{t}=6, 8, 12$, with a fixed lattice spacing $a=0.1361(20)$ fm, corresponding to temperatures of 242(4), 181(3), and 121(2) MeV, respectively. We explore a range of quark masses and spatial volumes with aspect ratios $N_{s}/N_{t}$ spanning from 2 to 4. By analyzing the mass and volume dependencies of the plaquette, plaquette susceptibility, chiral condensate, chiral susceptibilities, and Binder cumulant, we identify the pseudocritical transition quark masses from our largest lattice volumes. For $N_t=6$, this is 184(10) MeV (determined from the plaquette susceptibility). For $N_t=8$ and 12, the transition points vary slightly depending on whether the total or disconnected chiral susceptibility is used, yielding ranges of 36(1)-39.1(9) MeV and 3.5(3)-3.7(2) MeV, respectively, in the $\overline{\text{MS}}$ scheme at a scale of $\mu=2$ GeV. The negligible volume dependence at $N_t=6$ and 8, combined with finite-size scaling analysis at $N_t=12$ revealing volume growth significantly weaker than expected for a first- or second-order phase transition, points to a continuous crossover at these specific quark mass points. Additionally, we study the effects of residual chiral symmetry breaking on the chiral condensate and chiral susceptibilities using two different values of $L_s$.

We construct simple analytical solutions of the RG equations for the running couplings \alpha_s and y_{top} in the asymptotic regime. These solutions have an explicit form, contain only logarithms and no special functions, and subsequently sum up the leading, subleading, etc logarithms in all orders of PT. While the effect of y_{top} on the running of \alpha_s happens to be negligible, the role of \alpha_s on the running of y_{top} is essential, the account of higher orders gives a noticeable contribution.

We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal Möbius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes. As an application we write down closed-formulas for loop integrands in pure Yang–Mills theory, where the required cuts are generated by gluing $D$-dimensional tree amplitudes and summing over internal gluon states. We also use the two-loop five-point case as a validation, comparing with known integrand data and after integration-by-parts reduction, with known integrated helicity amplitudes. The same framework also produces compact cut-organized data for larger examples, including the two-loop six-point and three-loop four-point cases. We also describe the corresponding simplification in maximally supersymmetric Yang–Mills theory, where the absence of bubble and triangle subgraphs reduces the relevant cut poset substantially.

We construct the traceless components of the energy-momentum tensor on the lattice for QCD with $N_f=3$ flavours, such that their correlation functions satisfy the appropriate Ward identities in the continuum limit. To carry out this program, we define the theory on the lattice by the Wilson-plaquette and the $O(a)$-improved Wilson actions for gluons and quarks respectively. The discretization of the space-time entails that (i) the irreducible nonet representation of the SO($4$) group splits into a triplet and a sextet irreducible representations of the hypercubic group, and (ii) for each multiplet non-perturbative determinations of the the gluonic and fermionic renormalization constants are required. The bare gluonic components of the energy-momentum tensor are defined via the clover discretization of the field strength tensor, while the fermionic ones are discretized by appropriate combinations of symmetric covariant derivatives. Either for the triplet or the sextet representations, the two independent renormalization constants are then fixed non-perturbatively by imposing discretized versions of continuum Ward identities for one-point correlation functions in the presence of shifted boundary conditions and an imaginary chemical potential. The non-perturbative calculation is then carried out by Monte Carlo simulations, and the resulting renormalization constants are determined with a final accuracy of a few percent for values of the bare coupling constant squared in the range $0 \leq g_0^2\leq 0.96$.

We present a phenomenological study of quantum correlations in the decay of $B^0$ mesons into a system of two vector mesons. The decay of the $B^0$ meson into two vector mesons constitutes a bipartite system of two qutrits. The entanglement entropy is used as a measure of quantum correlations in the system of decaying particles. We study the variation of the Rényi entropy with Rényi order ($\alpha$) for the decay channels $B_s^0 \rightarrow \phi\, \phi$, $B_d^0 \rightarrow J/\psi\, K^{*}(892)^0$, $B_d^0 \rightarrow \phi\, K^{*}(892)^0$ and $B_s^0 \rightarrow J/\psi\, \phi$ and discuss the significance of entanglement entropy at different Rényi order regimes. The LHCb, ATLAS and Belle collaborations experimental measurements of complex polarization amplitudes and relative phases are used as input for our analysis. A comparison of entanglement entropy for all the $B^0$ meson decay processes, with both vanishing and non-vanishing phases, reveals a strong phase dependence of the entropy. We further present the results of Hartley entropy (Max-Entropy), von Neumann entropy, collision entropy, and min-entropy, each corresponding to different values and limits of the Rényi order. The comparison between the branching fractions of the decay processes and the von Neumann entropy shows a connection between entanglement and decay dynamics, indicating the role of weak and strong interaction in generating quantum entanglement. In addition, we evaluate several other entanglement measures, including linear entropy, I-concurrence, tangle, negativity, logarithmic negativity, Schmidt coefficients, and Schmidt rank for different $B^0$ meson decay processes. Our study demonstrates that entanglement measures provide useful insights into the underlying decay dynamics and may serve as important tools for understanding quantum correlations in high-energy particle physics processes.

Within single-field inflation, primordial black hole and scalar-induced gravitational wave production from enhanced primordial perturbations typically requires a transient non-attractor phase, such as ultra-slow roll. We investigate the physical consistency of modeling such scenarios through analytical Hubble-flow parametrisation. By reconstructing the underlying scalar field potential, we show that even slow transitions in the slow-roll parameters can hide sharp, localised spikes in higher-order derivatives of the potential at the transition from ultra-slow-roll to slow-roll. These are typically not found in analytic potentials. To evaluate the impact of these structures, we implement a UV-filtering procedure based on discrete Fourier transform to systematically suppress high frequency modes in field space in both classes of models. We find that the filter effectively removes sharp features in Hubble-flow-derived potentials. As a consequence, we show that UV-filtered models typically respect Wands duality invariance as the field evolves back from ultra-slow roll to slow roll. Beyond linear perturbation theory, the introduction of spurious UV effects might affect other observables, such as non-Gaussianity and loop contributions. Our results thereby question the robustness of simple analytical Hubble-flow parametrisation for modeling inflationary models with a transient non-attractor phase.

We study primordial-black-hole (PBH) dark matter in the two-dark-dimensions (2DD) framework, a six-dimensional brane-world scenario with two compact extra dimensions and a fundamental gravity scale of order $10\,\mathrm{TeV}$. We calculate the evolution of higher-dimensional PBHs including the recently proposed quantum-gravitational memory-burden effect. For a memory exponent $p=2$, the evaporation rate is strongly suppressed, allowing PBHs with initial masses as small as $\sim10^{-3}\,\mathrm{g}$ to survive until the present epoch. Consequently, PBHs can account for the observed dark matter over a mass range extending from $10^{-3}\,\mathrm{g}$ to $10^{21}\,\mathrm{g}$. We further compute the stochastic gravitational-wave background generated at second order by the primordial curvature perturbations responsible for PBH formation. We show that the conventional four-dimensional formalism for scalar-induced gravitational waves remains applicable throughout the mass range accessible to current and future gravitational wave experiments. The resulting signals can be probed by LISA, DECIGO, and pulsar timing arrays. Using Fisher forecasts, we find that these observations can constrain the PBH mass, dark-matter fraction, and width of the primordial curvature spectrum with high precision. The low fundamental gravity scale of the 2DD framework also permits the production of microscopic black holes at future high-energy colliders. Their decay signatures, together with gravitational-wave measurements, provide complementary tests of higher-dimensional gravity, the memory-burden mechanism, and primordial-black-hole dark matter.

Microstates of BPS AdS black holes have been studied from the classical cohomologies of the maximal super-Yang-Mills theories, but their quantum natures have been conjectural. It was recently found that a classical black hole (fortuitous) cohomology in the $SO(7)$ theory is lifted by 1-loop corrections. We show that such lifts also happen in the $SU(2)$ theory, presenting both lifted/unlifted examples. In particular, the lightest fortuitous cohomology and its `hairy' versions are unlifted, while many heavier `core' fortuitous ones are lifted. We argue that the entropy of classical cohomologies in the Cardy limit is larger than the indicial entropy of strictly protected states by at least $\approx 1.2 \%$.

We present $\texttt{SMaSH}$, a $\texttt{Mathematica}$ package to do spinor helicity computations in four spacetime dimensions $\href{https://github.com/aakash-kmr/SMaSH}{\text{(github)}}$. It can handle massive spinor helicity computations with explicit little group indices which is a novel feature. It can also handle massless as well as off-shell spinor helicity variables. It is designed to compute perturbative computations; it comes with predefined three point amplitudes and propagators for any masses and spins (arXiv:1709.04891). It can implement the high energy limit over an expression, check the discrete $\tt{C,P,T}$ transformations, compute contact terms and impose gauge invariance for any scattering process. We have shown the usage of such functions for computing gauge invariant Weinberg minimal amplitudes (arXiv:2506:12431, arXiv:2504:06343). The package can also generate both real and complex numerical kinematics for any $n$-point scattering for arbitrary masses and energy scales by implementing the $\tt{RAMBO}$ algorithm. It is also rich with basic spinor helicity manipulations like Schouten simplification, Clifford algebra manipulation, conversion between spinor helicity and Lorentz vectors, derivative w.r.t. spinors and their scalars, helicity scaling etc.

We introduce a two-dimensional $O(N)$ nonlinear sigma model with random Gaussian $p$-body interactions. The model combines the structure of a two-dimensional bosonic SYK-type quantum field theory with the stabilizing spherical constraint of the nonlinear sigma model. At large $N$ we derive the Schwinger-Dyson equations on a torus and analyze the solutions using both analytical approximations and numerical methods. We find a phase diagram qualitatively similar to that of the one-dimensional quantum spherical $p$-spin model, including a low-temperature transition to a spin glass phase. This phase is characterized by a finite Edwards-Anderson order parameter, while the dynamical part of the two-point function displays an approximate scaling regime. These results provide a tractable setting for studying approximate conformal behavior and glassy physics in a two-dimensional relativistic field theory with disorder.

We establish a refined Ryu–Takayanagi (RT) relation in AdS$_3$/CFT$_2$ using relative entropy as the central object, in place of the ultraviolet-divergent von Neumann entanglement entropy. Adapting Hollands' exact result for the chiral relative entropy to a diamond region, we express the boundary relative entropy between the vacuum and a coherent state as a Schwarzian functional, which the Fefferman–Graham dictionary identifies with the asymptotic data of a Bañados geometry; the rigidity of three-dimensional gravity promotes this boundary identification to the bulk. To linear order in the metric perturbation, the relative entropy then equals the variation of the RT geodesic length divided by $4G_N$. The construction rests only on the Bisognano–Wichmann/Borchers theorem and the holographic dictionary, giving a UV-finite, operator-algebraic counterpart to the RT relation.

We compute $\langle\hat{\Phi}^{2}\rangle_\text{ren}$ as well as the energy fluxes $\langle \hat{T}_{uu}\rangle_\text{ren}$ and $\langle \hat{T}_{vv}\rangle_\text{ren}$ (where $u$ and $v$ are the standard Eddington-Finkelstein coordinates) associated with a quantum massless real scalar field $\hat{\Phi}$, with a general curvature coupling constant $\xi$, near the inner horizon (IH) of a Kerr black hole, along the axis of rotation. The quantum field is in the Unruh state, corresponding to an evaporating black hole. We renormalize these quantities by the state-subtraction method. We drop the assumption of minimal coupling to the curvature, thereby generalizing the results of arXiv:2203.08502 for the fluxes at the IH. This requires understanding the asymptotic behavior of $\langle\hat{\Phi}^{2}\rangle_\text{ren}$ neat the IH. State subtraction allows us to push the computation of $\langle\hat{\Phi}^{2}\rangle_\text{ren}$ along the axis of rotation in the Kerr interior in arXiv:2409.17464 deeper into the near-IH region, exposing their final asymptotic behavior on approaching the IH. For $\langle\hat{\Phi}^{2}\rangle_\text{ren}$ (a $\xi$-independent quantity in the Kerr case), we find that the approach to its finite asymptotic IH value is given, per $\ell$-mode, by a ringdown phase (namely exponentially damped oscillations), followed by an inverse-power tail, both in the tortoise coordinate $r_{*}$ (which diverges at the IH). Interestingly, in the regime where the ringing dominates, the ringing's complex frequencies are (numerically) found to match twice the well-known classical quasinormal-mode frequencies in Kerr, and the inverse-power tails are found to be $r_{*}^{-2\ell-3}$ (resembling Price's law in the classical black hole exterior, upon replacement $t\to r_*$). [Abridged]

We consider the supersymmetric $\lambda$-deformation of $\text{AdS}_3 \times \text{S}^3 \times \text{T}^4$ superstrings and compute its perturbative bosonic tree-level worldsheet S matrix in the light-cone gauge. For generic values of $0 \leq \lambda < 1$, we show that the worldsheet scattering remains compatible with integrability due to a non-trivial cancellation of non-elastic scattering processes. By contrast, the S matrix becomes ill-defined for $\lambda \to 1$, despite the fact that this limit reproduces the non-Abelian T-dual geometry up to an analytic continuation. This suggests that the $\lambda \to 1$ limit does not capture the full worldsheet dynamics of the T-dual theory.

We initiate the classification of supersymmetric degenerate Killing horizons, with closed spatial cross section, away from the near-horizon limit in D=11 supergravity. We prove that all such solutions fall into two distinct classes, depending on lightcone chirality with respect to a Gaussian null coordinate system. For the first class of solutions, the negative lightcone chirality part of the Killing spinor is non-zero on the Killing horizon, and we prove that all such solutions are isometric to supersymmetric near-horizon geometries. In the second class, the negative lightcone chirality part of the Killing spinor vanishes on the Killing horizon. In this case, we prove that the spinorial Lie derivative of the Killing spinor with respect to the Killing vector which generates the Killing horizon vanishes, and that all such solutions with more than 13 supersymmetries are pp-waves.

The maximally transcendental, or most complicated, terms of gauge-theory scattering amplitudes have long been singled out, following Lipatov and collaborators, as those parts of a QCD amplitude that most closely mirror maximally supersymmetric Yang–Mills theory. We report on a programme that turns this observation into a practical computational tool. We show that the rational prefactors multiplying the highest-weight special functions of planar QCD amplitudes are governed by four-dimensional leading singularities, which can be classified and evaluated using on-shell diagrams. The resulting prefactors are manifestly conformally invariant and admit compact spinor-helicity expressions that hold for arbitrary multiplicity. Combining this input with the recently established two-loop six-particle function space, we set up a symbol bootstrap and determine, for the first time, the maximal-weight symbol of the planar two-loop six-gluon amplitude in massless QCD, first for the ${-}{-}{+}{+}{+}{+}$ helicity configuration and subsequently for all MHV configurations. The answer is fixed uniquely by physical consistency conditions, requires a reduced alphabet of only $137$ symbol letters, and yields as a byproduct previously unknown two-loop triple-collinear and double-soft splitting functions. We summarise the method and the results, and outline the directions they open up.