Papers

The supersymmetric index, which gives a signed count of the microstates of black holes, can be computed directly from a gravitational path integral with appropriate boundary conditions. From general arguments based on the supersymmetry algebra, the index is expected to be independent of the temperature and, away from walls of marginal stability, of the asymptotic values of the scalar moduli. On the gravity side, this has been verified by explicit computations in many examples, but a general proof is lacking even at the classical level. We fill this gap by showing that in any four-dimensional supergravity theory with $\mathcal{N} \geq 2$ supersymmetry in asymptotically flat space-time, the classical contribution to the index from each supersymmetric saddle is independent of both. The argument uses only the behavior of the solution and of the Killing spinor equations near infinity. The result therefore holds in the presence of arbitrary higher-derivative corrections and for multi-centered black hole configurations. In particular, moduli independence follows without appeal to the attractor mechanism, which relies on the near-horizon geometry.

We study the thermodynamics of the BMN matrix model at large $N$ and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional $SO(9)$ gauged supergravity, the static $SO(3)\times SO(6)$-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of $\mu/T$, which power-law fits place at $4\pi$ with an estimated uncertainty below $10^{-10}$. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the $2/5$ power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.

We study the spherical geometry from the Simpson-Visser prescription $r\to\sqrt{r^2+a^2}$ to the quantum Oppenheimer-Snyder-Datt (qOSD) black hole of loop quantum cosmology, whose lapse function $A=1-2M/R+\alpha M^2/R^4$ carries the correction $\alpha$. This family interpolates between the qOSD black hole ($a\to0$), the Simpson-Visser black bounce ($\alpha\to0$), and Schwarzschild. The geometry is regular for every $a>0$, the Ricci scalar at the throat is blind to $\alpha$ while the Kretschmann scalar is not, and the null energy condition is violated at the throat by $-1/(4\pi a^2)$. The $(\alpha,a)$ plane splits into a two-horizon regular black hole, a single-horizon black hole with a hidden bounce, no Cauchy horizon, and a traversable wormhole; the middle region removes the mass-inflation channel of regular black holes without fine tuning. Because circular orbits are governed by the areal radius, photon sphere, shadow, ISCO and azimuthal epicyclic frequency depend on $\alpha$ only, whereas the Lyapunov exponent and radial epicyclic frequency carry the factor $\sqrt{1-a^2/R^2}$: shadow constrains only $\alpha$, while ringdown damping and the twin-peak quasiperiodic-oscillation ratio are sensitive to $a$. We derive horizon thermodynamics with a first-law entropy that departs from the area law, show that the bounce changes the thermodynamic topological charge from $W=-1$ to $W=0$ at every $\alpha$, and compute scalar, electromagnetic and Dirac quasinormal spectra using third-order WKB, Chebyshev spectral collocation and time-domain integration, which agree with one another and with eikonal scaling. Greybody bounds, Hawking emission, cascade sparsity and ringdown quality factor complete the analysis, and in the wormhole region the double-peaked potential produces echoes.

We describe construction of gravitationally dressed observables in de Sitter (dS) space, to leading non-trivial order in Newton's constant. We show that for an underlying field theory observable to be "gravitationally dressable," it must be dS invariant. If it satisfies this condition, its gravitational dressing can be constructed in terms of certain Green functions, by solving the condition that the dressed observable commute with the constraints. We provide a construction of the Green functions relevant for dressing observables lying on a time-symmetric slice. A simple example of a dS invariant observable is an operator creating a two-particle state of scalars. In the large mass limit, the particles are shown to be antipodally located, and the dressing of this operator (or corresponding state) can be explicitly constructed. Its behavior is diagnosed by certain correlators involving this state, and we check explicitly that these correlators then reproduce a linearized version of the Schwarzschild-dS solution. The underlying dS-invariant observables may be thought of as relational, and we argue can be generalized to include systems with properties of observers, which then could be likewise gravitationally dressed. We also briefly describe how such dressed observables can be related to alpha vacua, and discuss other questions regarding a more complete construction and role of such operators.

We propose an extension of the cosmological-state construction of Antonini, Sasieta and Swingle (AS$^2$) to three or more holographic CFTs. Each CFT resides on the asymptotic boundary of an AdS page, and all pages are glued along a common interface by imposing the multiway junction conditions. The associated states are prepared by Euclidean evolution with a multilinear insertion. In appropriate heavy insertion limit the bulk geometry develop a closed universe in the center and we refer the state in this limit as a booklet cosmological state. Extending the effective Gaussian assumption used in AS$^2$, we model the three-page insertion by a circular complex Gaussian random tensor, yielding a tripartite Haar state in flat energy windows. In this Gaussian model of the cosmology-to-boundary map, each arm is a network branch associated with one boundary CFT. In the simplest example of three pages with three equal output Hilbert-space dimension $b$, we show that a prescribed code of dimension $K$ is approximately recoverable from any two arms, with vanishing error and high probability as $K/b\to0$.

We derive the canonically normalized modes of a two-field inflationary system with arbitrary constant quadratic mixing and unequal sound speeds $c_\varphi$ and $c_\sigma$ for the curvature and isocurvature perturbations, respectively. A Laplace representation reduces the coupled dynamics to a second-order Heun equation and gives the exact late-time curvature power spectrum for arbitrary values of the mixing parameter and entropy mass. The sound-speed ratio $r_c=c_\sigma/c_\varphi$ controls the separation between the two sound horizons. At fixed nonzero mixing and $r_c\ll1$, the power exhibits power-law enhancement, growth as $\ln^2(1/r_c)$, or bounded oscillations in $\ln r_c$, depending on the mass and mixing. For $r_c\gg1$, the correction to the unmixed spectrum vanishes as $\ln r_c/r_c^2$ at fixed mass and mixing. Using the same normalized modes, we compute the tree-level bispectrum for three representative cubic interactions, with the mixing parameter treated exactly. For heavy entropy fields, unequal speeds modify the collider amplitude and phase while preserving the strict squeezed frequency set by the final entropy mass. The power-normalized amplitude can vary nonmonotonically with $r_c$, and a sound-speed hierarchy can delay the approach to this asymptotic regime.

Recent work has shown that maximal supersymmetry, combined with a particular scalar-parity condition at six points, imposes nonlinear constraints on four-point effective field theory amplitudes. Numerical bootstrap studies incorporating unitarity provide evidence for the Veneziano amplitude in maximally supersymmetric Yang–Mills theory and for the Virasoro–Shapiro amplitude, together with infinite-spin alternatives, in supergravity. In this paper, we establish these constraints to all orders in the low-energy expansion. The derivation uses a collinear limit in which three three-particle factorization channels, or six in gravity, simultaneously go on shell. A scalar-parity projection and a single discrete R-symmetry eliminate the unknown six-point remainder, leaving three-term master equations determined entirely by four-point factorization. Solving these equations proves the conjectured exponential forms and provides a map that reconstructs the full amplitude from its regular forward limit. Under explicit analytic and positive dispersive assumptions, the fixed reflection-even part of the gauge-theory exponential determines the forward spectral measure and uniquely selects the Veneziano amplitude, with finite-spin residues emerging as a consequence. In gravity, the exponential leaves the forward measure undetermined: a measure supported at a single massive level reconstructs an amplitude with infinitely many exchanged spins at that mass. Finite-spin support at the lowest massive pole is therefore an additional assumption required to select the Virasoro–Shapiro amplitude within the stated ultraviolet framework.

Deriving simple and accurate three-flavor neutrino oscillation probability formulas in matter is critical for understanding the phenomenology of upcoming experiments. In this article, we extend the Jacobi diagonalization method for deriving effective parameter mappings for neutrino oscillations in matter. The key insight behind the extension is to purposefully parameterize the mixing matrix, $U_{\text{PMNS}}$, using particular arrangements of Euler rotations. This novel extension allows for deriving simple and accurate effective mixing parameter mappings for exotic types of matter potentials. First, we revisit the Jacobi diagonalization method for neutrino oscillations with standard matter effects and use this to demonstrate our generalization. Subsequently, we apply the Jacobi diagonalization method to scalar non-standard interactions (SNSI) and derive effective parameter mappings for all three single diagonal coupling cases. The resulting formulas reveal that all diagonal SNSI couplings could give rise to a scalar MSW (SMSW) effect, that is an energy independent resonant enhancement analogous to the MSW effect. Finally, we study the accuracy of the derived SNSI formulas for various contemporary and upcoming experiments. For $\delta m_{ee}$, the accuracy is excellent for all considered experiments. For $\delta m_{\mu\mu}$ and $\delta m_{\tau \tau}$ the accuracy is worse since $A_{CC}$ must be neglected, and first order perturbative corrections are applied to amend this.

Schur sampling is a fundamental primitive for extracting permutation-invariant information from many-body quantum systems and has broad applications in quantum information science. Circuit-based implementations typically rely on coherent representation-theoretic operations such as Clebsch-Gordan transforms, generalized phase estimation, or quantum Fourier transforms over the symmetric group. We show that unitary Schur sampling of arbitrary permutation-invariant mixed states on $n$ $d$-dimensional qudits can instead be implemented using only pairwise SWAP tests, namely, two-qudit projective measurements onto the symmetric and antisymmetric subspaces. Our protocol achieves error $\epsilon$ in diamond distance using $O(n\min\{n,d\}^{3}\log^2(n/\epsilon))$ random SWAP tests. The central idea is to repeatedly identify and extract the largest antisymmetric subsystem. This turns unitary Schur sampling into a search for antisymmetry and gives the algorithm a natural interpretation as a stochastic traversal of a Young diagram. The protocol preserves the $\mathrm{SU}(d)$-irrep state while preparing a canonical pure state in the multiplicity subsystem. As an application, we consider quantum purity amplification (QPA), in which multiple noisy copies of a pure quantum state are combined to produce a state of higher purity. We show that the optimal purified state can be obtained by retaining a single designated output qudit and discarding the rest.

Electromagnetic duality in the toric code has order two at the level of anyon types and acts as a Hadamard-type logical transformation on the encoded quantum information. Here, we ask whether it can likewise be realized microscopically as an order-two Clifford operation. For the $\mathbb{Z}_2$ toric code, we prove that any locality-preserving Clifford realization of electric-magnetic exchange cannot have order two. Our proof is fully general and requires neither translation symmetry with restricted families of system sizes nor a fixed pairing between vertex and plaquette stabilizers. Geometrically, the proof locally emulates the unavoidable crossing between electric and magnetic strings, similar to a cross-cap in a non-orientable manifold. Extending the problem to the $\mathbb{Z}_N$ toric code, we find that an order-two Clifford realization exists for odd $N$, whereas it is impossible for even $N$. Our results show that the group law of an emergent electromagnetic duality need not lift faithfully to its microscopic Clifford realization.

We present a global determination of the six long-distance matrix elements (LDMEs) within non-relativistic QCD (NRQCD) appearing in the production of prompt $J/\psi$ up to $\mathcal{O}(v^2)$ using high-$P_T$ LHC data for direct and feed-down contributions from $\chi_c$ and $\psi(2S)$. Using a leading-power fragmentation framework at NLO+NLL, we fit $\psi(2S)/J/\psi$ yield ratios from ATLAS and CMS and $\psi(2S)$ CMS polarization data at $\sqrt{s} = 13$ TeV, injecting one decay width per charmonium. The fit LDMEs provide excellent predictions of the CMS and ATLAS cross-section data up to $P_T=360$ GeV for the $J/\psi$, as well as the $J/\psi$ polarization data from CMS. The obtained excellent agreement with production and decay data demonstrates that $\mathcal{O}(v^2)$ NRQCD is sufficient to describe $J/\psi$, $\psi(2S)$, and $\chi_c$ hadroproduction at large $P_T$.

An outstanding question in holographic superconductivity is how rotation and non-relativistic scaling symmetries compete to modify the onset of condensation. We address this by comparing the probe superconductor sectors of two exact rotating axionic black holes: a four-dimensional asymptotically anti-de Sitter solution dressed by a non-minimally coupled scalar, and a five-dimensional asymptotically Lifshitz solution with $z \in (2,3)$. Writing both metrics in a common stationary form yields a master scalar equation in which rotation enters through the co-rotating potential $A_t-N^xA_x$. This equation explains why the temporal and spatial components of the probe gauge field cannot be treated independently. The numerical profiles reported in [1,2] indicate that the correlated deformation associated with rotation reduces the condensate amplitude in both backgrounds, whereas increasing the dynamical exponent at fixed $J$ enhances the Lifshitz condensate. Since the parameters $\alpha$ and $J$ also modify the matter fields supporting the corresponding exact geometries, these trends should be interpreted as properties of complete correlated families rather than as universal effects of mechanical rotation alone.

We develop a gauge-invariant effective field theory for scalar glueball interactions based on the Yang-Mills gluon condensate. Starting from a coherent-state formulation of the Yang-Mills vacuum, we derive an effective Lagrangian for the scalar glueball and its interactions with gluons. The resulting crossing-symmetric amputated four-gluon Green's function is projected onto the color-singlet $J^{PC}=0^{++}$ channel, yielding a normalized scalar glueball form factor that factorizes into universal kinematic structures and an intrinsic glueball function. The formalism predicts a parameter-free effective interaction radius for the ground-state scalar glueball with resonance $f_0(1710)$, $r_{\rm int}=\sqrt{6}/m_\phi=0.28$ fm, which is in excellent agreement with recent lattice Yang-Mills determinations of the mass-radius ($r=0.263(31)$ fm). The predicted momentum dependence of the normalized form factor is consistent with lattice Yang-Mills gravitational form factor data, with the $f_0(1710)$ candidate providing the best overall fit and $r_{\rm int}$. Inclusion of the first excited $0^{++}$ glueball produces modest corrections to the interaction radius ($r_{\rm int}^*=0.240$ fm) while yielding stable and kinematically robust modifications of the form factor. This framework provides a systematic bridge between effective field theory and first-principles lattice Yang-Mills calculations of scalar glueball dynamics.

In this paper, we extend the paradigm of the Geometrical Trinity of Gravity to the Carrollian geometry to construct a comprehensive framework of dynamically equivalent theories for Magnetic Carrollian gravity. Utilizing the inherent ambiguities and freedoms of affine connections on degenerate metrics, we systematically relax the metric-compatibility and zero-torsion constraints of the rigid magnetic sector. By imposing global flatness on these modified connections, we prove that the curvature of a Magnetic Carrollian universe can be dynamically traded for isolated kinetic energy densities of torsion and non-metricity. Unlike the Lorentzian Trinity which maps gravity to alternative gravitational frameworks, the Carrollian equivalences can also map spacetime geometry to non-gravitational theories. Specifically, we demonstrate that intrinsic torsion recovers Electric Carrollian gravity as the Teleparallel equivalent of Magnetic Carroll gravity; purely spatial torsion reproduces kinetic terms stracturally similar to the magnetic Hamiltonian of scalar-charge Fracton gauge theory; and temporal torsion sectors map independently to $U(1)$ Maxwell electric fields and Carroll-Weyl conformal dilaton theories. Finally, by formulating a Symmetric Teleparallel Carroll connection with minimal non-metricity, we show that the Magnetic Carrollian Lagrangian is dynamically equivalent to an ultralocal, isotropic Electric Carrollian gravity upon exploiting the present freedoms in connection. These results establish a geometric dictionary translating Carrollian gravitational dynamics into the language of tensor gauge theories, electromagnetism, and dilaton theory.

In this paper, we present an algorithm for constructing all Calabi-Yau orbifolds and their mirror pairs associated with an arbitrary Berglund-Hubsch-type model, and prove its correctness. In particular, the proposed method yields explicit generators for the groups defining the corresponding orbifolds. The method for classifying maximal admissible groups is proposed. We illustrate the application of the classification approach to an arbitrary Fermat-type Calabi-Yau manifold. In addition, as an illustrative example, we classify all maximal admissible groups of Fermat-type Calabi-Yau threefolds.

Motivated by applications to low-dimensional worldsheet string constructions, we analyze $\mathcal{N} = 1$ super Liouville theory on the torus. Specifically, we re-examine the recursive representations of the torus one-point super Virasoro blocks that have been constructed in the literature and correct several of their ingredients. In the process we identify a new block in the odd spin structure, associated with a privileged superdescendant whose torus one-point function transforms like that of a Virasoro primary. We then demonstrate that the structure constants for both spacelike and timelike super Liouville theory satisfy modular crossing. Furthermore, we use a bootstrap argument to construct modular crossing kernels for all four spin structure sectors, valid for central charges $c \in \mathbb{C}\setminus(-\infty,\tfrac{3}{2}]$, and verify that they correctly implement the crossing transformations of the blocks. As a concrete application of the technology, we analyze the super Virasoro minimal string. There are four such theories, $\mathrm{0A}^{\pm}$ and $\mathrm{0B}^{\pm}$, which are distinguished by the GSO projection together with the choice of worldsheet supercharge. The resulting NS-sector sphere three-point and torus one-point amplitudes are shown to agree with topological recursion on the spectral curves of the dual matrix integrals, which were recently derived from 3d supergravity. Notably, the one-point function of the privileged superdescendant plays an essential role in the contribution of the odd spin structure to the torus amplitude via a careful treatment of the picture changing operator. We also identify an exceptional zero-momentum Ramond insertion in the $\mathrm{0A}^{-}$ theory that we interpret geometrically as a Ramond puncture, and match its mixed sphere three-point amplitude to the corresponding intersection theory prediction.

We study coherent release from a finite serial Krylov sector into an exact conformal tail with asymptotically linear Lanczos coefficients. We derive the cumulative occupation up to a cut that moves to greater Krylov depth with time, tracking the probability accumulated behind the propagating front. This quantity separates the release dynamics of the finite sector from subsequent propagation through the tail. The tail sets the logarithmic transit scale, while the finite sector shapes the resulting distribution. The early edge records the number of serial steps before emission, while the late edge reflects slow resonances and interference and can also exhibit logarithmic enhancements. Thus, one- and two-site sectors can share the same leading resonance in their continued-fraction descriptions yet produce distinct cumulative occupation patterns. We illustrate this framework in thermal AdS$_2$, where a dressed oscillator yields, in the weak-coupling limit, a two-site shallow sector coupled to the conformal tail.

Near threshold, intra-tower decays of Kaluza-Klein (KK) gravitons are pure $d$-wave, with rate $\Gamma \propto p^5$ in the decay products momentum $p$, rather than the $s$-wave $\Gamma \propto p$ assumed in the dark dimension literature. In a flat dark dimension this excludes KK gravitons as a dark matter candidate. Even if some other source of dark matter is assumed, the irreducible freeze-in abundance of KK gravitons produce MeV gamma rays which allows one to set upper limits on the reheating temperature; additionally using the lower bound on the reheating temperature from big-bang nucleosynthesis and the cosmic microwave background requires the radius of the extra dimension to be almost three orders of magnitude smaller than the distance conjecture would naively prefer, $R\sim \Lambda^{-1/4}$.

We derive a generalized fluctuation-dissipation theorem (FDT) for vector fields in rotating thermal equilibrium from an exact phase-space Kubo-Martin-Schwinger (KMS) relation. The resulting FDT contains rotation-induced tensorial contributions beyond a scalar thermal factor. In the local transport limit, we obtain a model-independent generalized Einstein relation with rotation in which, through second order in thermal vorticity, symmetric momentum diffusion depends on low-frequency spectral information beyond that encoded in the rotation-dependent dissipative drag. Remarkably, we find a new Einstein-type relation linking zero modes in the spectral function to the nonrotating drag coefficient. These zero modes underlie a new mechanism for the orbital polarization of heavy quarkonium. The same FDT constraint yields a modified detailed-balance relation whose first-order vortical correction is governed by transition polarization, without explicit dependence on the bath model. Our findings establish microscopic equilibrium constraints for studying rotating quantum matter in various fields.

We discuss the triality between stochastic growth models in the KPZ universality class, the DSSYK model, and low dimensional dilaton gravity. The TASEP model, which will be our primary focus, is identified with the strong-coupling limit of two-dimensional quantum gravity. The Hamiltonian of DSSYK and the transfer matrix of ASEP coincide up to an additive constant, and we derive the exact expression for the resolvent of the corresponding transfer matrix in ASEP on a finite interval. We also mention the relation of cumulants with the Tutte polynomial $T(1,q)$ of the crossing graph dual to the chord diagram, which implies the relationship of the models considered with the $Q=0$ Potts model coupled with gravity. We further exploit the realization of all these models in terms of different versions of discrete and continuous random walks on two-dimensional manifolds, which parameterize the Hilbert spaces of the respective theories. The representation of TASEP as the growth model of heaps provides new insight into strong-coupling gravity, suggesting its interpretation as an emerging phenomenon. The new dualities between ASEP and q-TASEP models and heap models providing a useful growth interpretation have been developed.

Hidden zeros impose constraints on scattering amplitudes beyond their familiar factorization properties. We explore their structure in two related directions. We first promote hidden zeros to explicit splitting formulas that organize full amplitudes at generic kinematics. Ordered $\mathrm{Tr}(\phi^3)$ amplitudes, nonlinear sigma model (NLSM) amplitudes, and cosmological wavefunctions share the same defining exact splitting structure $\mathcal A=\sum_\alpha R_\alpha\, {\mathcal J}_{\alpha,L}{\mathcal J}_{\alpha,R} {\mathcal J}_{\alpha,\mathrm{out}}$, adapted to any hidden zero. Each prefactor $R_\alpha$ is a condition of the hidden zero locus, so this decomposition manifests the hidden vanishing term by term. The remaining factors are lower point amplitudes or currents. Using these representations, we can systematically find new zero loci beyond the usual ones. In particular, we obtain five new all-multiplicity zero families. We also find continuous families of zeros: the coefficients of their defining equations can vary continuously while the amplitude remains zero.

We derive the tree-level interaction vertices of the linear sigma model with quarks in the presence of global rotation. Starting from the scalar and fermionic field solutions in a rotating background, we construct the corresponding spectral representations and use them to evaluate the mesonic self-interactions and Yukawa couplings of the model. We show that rotation modifies the usual momentum-space structure of the interaction vertices: conservation of longitudinal momentum is accompanied by angular-momentum selection rules, while the transverse dynamics is encoded in rotation-induced radial form factors involving products of Bessel functions. The resulting expressions provide a set of interaction rules adapted to the symmetries and finite geometry of the rotating system. Although derived within the linear sigma model with quarks, the structures obtained for scalar self-interactions and scalar-fermion couplings can be extended to a broader class of quantum field theories under global rotation. These results provide the building blocks for perturbative calculations and contribute toward a microscopic quantum-field-theoretical description of interacting matter in rotating environments.

This work presents a unified inflationary and late-time cosmology, developed within Einstein-Gauss-Bonnet gravity coupled to three scalar fields, governed by a single potential and coupling function throughout cosmic history. Permitting the Gauss-Bonnet coupling to depend on the field content, rather than assigning it arbitrarily, produces a two-phase inflationary scenario: the higher-curvature term initially drives expansion and later becomes a subdominant. The initial super-inflationary stage ends dynamically when the geometrically induced stabilization of the waterfall field fails, at a field value determined by the combination $(n-1)Q$. Coherent oscillations of the waterfall condensate serve as the initial radiation source, replacing conventional reheating and establishing the thermal bath necessary for the subsequent warm phase. Utilizing a two-stage dissipation mechanism with $\Gamma_\phi\propto T^3$, the scalar and tensor spectra are derived while retaining Gauss-Bonnet contributions, demonstrating that the growth of inflaton fluctuations is regulated by the shear viscosity of the bath, which is essential for model viability. A quartic potential, previously excluded in the cold scenario, becomes viable, with $n_s$ within the Planck $1\sigma$ band and $r$ suppressed. Agreement with the spectral index is generic, while internal consistency confines the model to a narrow band in $(n-1)Q$. Finally, the release of the third scalar near matter-radiation equality transforms a very small mass scale into a very large coupling by a logic inverse to the seesaw mechanism. At late times, the inflaton persists as dark energy.

In the quantum inverse scattering method, the sine-Gordon model is solved on a lattice, and its continuum and infinite-volume limits become uniform only after the length of the box is rescaled. We show that this rescaling, supplemented by an on-shell condition, defines a renormalization scheme. The whole dependence on the cut-off is absorbed into a factor $Z_L$ multiplying the length of the box, with an exponent fixed by the scaling dimension of the vertex operator; neither the field nor the coupling $\beta$ is renormalized, no subtraction scale is introduced, and the mass parameter receives a finite renormalization, fixed by requiring that the lightest breather has the mass of the boson in the linearized theory. The soliton and breather masses follow from the eigenvalues of the monodromy operator as functions of parameters that do not run, and reduce to the classical and semiclassical results as $\beta\rightarrow0$. In particular, the mass ratios are produced directly from the regularized construction, while the relation between the lattice parameters and the physical scale is absorbed into $Z_L$ and never needs to be computed. The scheme is a reparameterization of the theory which makes explicit the interplay between integrability and renormalization. We compare it with Coleman's normal ordering and with conformal perturbation theory, and we argue that it extends to ultralocal integrable theories with a massive spectrum, possibly including asymptotically free models that admit an ultralocal lattice regularization.

We study how driving history affects the nonlinear topological relaxation of a holographic superfluid. Different histories are constructed to reach the same present driving conditions and then follow the same future protocol. Although they relax to the same final winding sector, their late-time dynamics remain strongly history-dependent: the residence time of the penultimate winding sector changes by about a factor of \(3.7\). This variation is organised by the modal imbalance carried into the common amplification stage. Histories with different shapes but matched modal imbalance produce nearly identical relaxation times. The same qualitative behaviour is found for a second pair of competing modes.

Ringdown spectroscopy probes black hole (BH) dynamics, and exceptional points (EPs) can reveal underlying degrees of freedom. We develop a procedure to identify EPs in ringdowns using a time-weighted Jordan term and a splitting bound. For relative Jordan excitation proportional to separation, we derive a sixth-order squared distance between split and EP waveforms after fitting the resonance center. Independent constraints on these quantities can restore fourth order. Complete waveforms show that omitting ordinary responses can strengthen EP evidence and spuriously tighten splitting bounds.

We analyze the correlations of the vacuum state of a charged scalar field by constructing localized observables in two disjoint regions. We consider a time-dependent homogeneous electric field and examine the time evolution of correlations by relating it with the particle-antiparticle creation through the Schwinger effect. Our results show that the electric field increases the mixedness of the states and enhances total correlations, while the distillable entanglement among the regions decreases, vanishing at a finite time for sufficiently intense pulses within the non-perturbative pair-production regime. We also discuss the effect of anisotropy induced by the external background, showing that the distribution of correlations acquires a nontrivial directional dependence.

Non-abelian infrared radiation can be seen as both a practical ingredient for QCD phenomenology and a window on the long-distance structure of gauge theories. During the last decade, a novel viewpoint was developed on infrared phenomena: soft currents are seen as arising from asymptotic symmetries realised on the celestial sphere, and soft colour correlations similarly emerge from a two-dimensional conformal field theory on the sphere. In this contribution, we briefly review the status of this approach. We begin with the standard bulk picture, presenting the infrared factorisation of massless scattering amplitudes, and then we show how universal infrared information gets mapped to marked points on the celestial sphere. In particular, soft colour-dipole singularities are reproduced to all orders by a correlator of vertex operators in a free-boson theory on the sphere. We then proceed to study soft-gluon currents, and show how bulk results constrain the structure of the celestial theory beyond the free-field limit. For single emission, we note that all logarithms in dipole-like loop contributions can be absorbed into the choice of scale for the strong coupling. For multiple emission, we show how the emerging mixed-helicity celestial operator product expansion must be weighted by energy fractions, breaking holomorphic factorisation and obstructing associativity under successive collinear limits. These results illustrate a remarkable connection between the familiar physics of infrared QCD and the dynamics of a two-dimensional theory on the celestial sphere.

We revisit the problem of defining natural torsion and curvature tensors for generalised connections and of using them to reconstruct the effective action for the massless modes of the closed string from generalised geometry. The starting point is the description of a Courant algebroid as a differential graded (dg) symplectic manifold. A systematic procedure for split dg manifolds singles out a generalised Lie bracket as part of a larger Lie 2-algebroid structure, with the right properties to unambiguously define torsion and Riemann curvature tensors together with their corresponding Bianchi identities. This framework eliminates the structural circularity and ambiguity problems of previous approaches in the literature. We show that a unique generalised metric compatible generalised connection with fixed (con)torsion exists for any choice of ordinary connection that splits the dg manifold, while at the same time all Lie 2-algebroids obtained in this way are equivalent up to $L_{\infty}$ quasi-isomorphisms. For a given Lie 2-algebroid we demonstrate that the unique compatible generalised connection reproduces the effective closed string action from a geometric action based on the new generalised Ricci tensor upon making a canonical choice of torsion.

We propose an analyticity bootstrap method to determine the reduction of Feynman integrals (FIs). The key observation is that, at any kinematic point, a dimensionally regularized FI possesses a Taylor expansion region (analytic region), and the finiteness of the Taylor region strongly constrains the integral reduction coefficients, which are rational functions of the kinematic variables. By writing the most general ansatz compatible with the singularity structure and then fixing the remaining parameters with only a few integration-by-parts (IBP) samples or asymptotic expansions, one can obtain the full reduction. We develop the method systematically in both single-variable and multi-variable cases, with many explicit examples. Interestingly, the differential equations (DEs) of the master integrals determine all these analyticity constraints and, conversely, the constraints facilitate the construction of the DEs. In particular, we show that the DEs in the auxiliary mass flow method can be constructed at significantly reduced cost and can even be fully determined without using IBP.