Motivated by the problem of understanding the experience of an observer in dynamical quantum gravity, we study the effects of coupling a one-dimensional quantum mechanical system living on a bulk worldline to Euclidean AdS JT gravity. On the disk topology, where the worldline stretches between two boundary points, we derive exact expressions for the Euclidean propagator of the observer and for its correlation functions, and discuss their holographic interpretation. The main effect on the quantum mechanics is the fluctuation of the total Euclidean time for which the observer evolves, or its inverse temperature for closed Euclidean paths. This turns the standard quantum mechanical evolution operator into an average of those, weighted by a measure over Euclidean times which in the semiclassical limit is peaked around the geodesic distance between the boundary points. We characterize the fluctuations around this value, finding that they are small compared to the mean, but large compared to the effective Planck scale of the model. These fluctuations can be resolved by an observer with a finely spaced density of states. We also discuss the Lorentzian interpretation of these Euclidean calculations. Finally, we compute a contribution to the partition function of the observer coupled to gravity coming from the double trumpet. In this case the fluctuations of the effective temperature are large, reflecting the absence of a smooth semiclassical saddle point.

The de Sitter horizon behaves in a qualitatively different way from a black hole horizon, which poses a challenge to any attempt to develop a fundamental quantum description of de Sitter space. In this paper we gather some ``data'' on this problem using gravitational calculations, seeing that they lead to an ``anti-scrambling'' phenomenon that is contrary to the behavior of standard many-body quantum systems. We organize our discussion in terms of correlation functions computed on the worldline of an observer living in the spacetime, with the two-point function looking like a conventional thermal correlator but the four-point function showing anti-scrambling. We propose that anti-scrambling can be realized in a quantum system whose Hamiltonian is bounded from both above and below using correlators that are folded in Euclidean time.

We study the two-dimensional Ising model deformed by the relevant thermal operator and placed on de Sitter (dS) spacetime. Despite being strongly interacting in its original formulation, the theory is exactly solvable on account of fermionisation. We compute exact cosmological correlators and compare them with conformal perturbation theory. In the Euclidean formulation of the model, we first compute the renormalised sphere partition function and the exact two-point functions of the thermal operator and descendant-like operators. We analytically continue the two-point functions to Lorentzian dS$_2$. Their late-time behaviour is governed by de Sitter representation theory and includes oscillations associated with principal-series scaling dimensions. We then analyse two-point functions of the spin and disorder operators, which are non-local in the fermionic variables, and derive non-perturbative constraints on their late-time scaling dimensions. In both cases, we compare the exact answers to conformal perturbation theory (CPT) and we show that divergent secular terms generically spoil the perturbative series at late times. The de Sitter Ising model shows explicitly how late-time perturbative pathologies are resummed in non-perturbative cosmological observables and provides a minimal solvable laboratory for quantum field theory dynamics in de Sitter space.

We study the dynamics of Krylov state complexity in finite-dimensional quantum systems. Orthogonal polynomials built on a discrete energy spectrum crowd away from regions where the density of states is low at large Krylov index. The physical implication of this result is that, even using a minimalist Krylov state complexity which is defined over the entire spectrum, the Krylov complexity provably stops growing a little past the Heisenberg length in every low-energy state. This has interesting implications for the proposal that Krylov complexity is related to the wormhole length in 2D quantum gravity.

We study the space of four-dimensional ultraviolet completions for $\mathcal{N}=8$ supergravity that are described at low energies by weakly-coupled effective field theories (EFTs) with maximal supersymmetry and $\mathrm{SU}(4)\times\mathrm{SU}(4)$ R-symmetry. We show that tree-level factorization of the 4-, 5-, and 6-point EFT scattering amplitudes, together with a certain ``peculiar parity'' condition, leads to nonlinear constraints on the 4-point Wilson coefficients. This peculiar parity is a property that can only be imposed on a subset of scalar amplitudes. Combining the nonlinear constraints with positivity, we find that the allowed region of 4-point Wilson coefficients is reduced to a non-convex domain with two sharp corners: one being the closed superstring Virasoro--Shapiro amplitude, the other an infinite spin tower amplitude exchanging states of every spin at the same mass. We show both numerically and analytically that requiring a finite number of states near the first mass level leaves only the Virasoro--Shapiro amplitude.

Spacelike singularities supported by matter satisfying the null energy condition (NEC) are expected to fall within the Belinski--Khalatnikov--Lifshitz (BKL) paradigm. We show that controlled violations of the NEC in holography can lead to different black hole interiors. In a holographic model dual to a strongly coupled non-Hermitian $\mathcal{PT}$-symmetric QFT, we uncover a novel non-Kasner regime within its real, $\mathcal{PT}$-restored phase. The deep-interior geometry describes an isotropic FLRW cosmology undergoing super-accelerated expansion and approaching a Little Rip. This regime leaves a characteristic imprint on two-sided heavy-operator correlators, allowing it to be distinguished from a standard Kasner interior. Our construction provides a concrete holographic realization of a Little Rip cosmology and lays the groundwork for a Little Rip/CFT correspondence, in which such cosmological regimes can be explored through observables in a non-Hermitian quantum field theory.

Black hole thermodynamics for generic dynamical, non-equilibrium regimes remains a fundamental challenge. We establish dynamical entropy as the Noether charge associated with a generic evolving null surface subject to Dirichlet boundary conditions. We uniquely specify the symmetry generator associated with the dynamical entropy, which is a null vector on the null surface, upon requiring physically motivated geometric conditions that yield a notion of ``dynamical zeroth law.'' We prove that this Noether charge density satisfies the second law of thermodynamics strictly at each instant in time, bypassing the teleological final conditions traditionally required by event horizons. Thus, we extend and generalize the notion of dynamical entropy introduced in \cite{Hollands:2024vbe}, in some different ways: We do not impose background stationarity; our dynamical entropy and the associated second law are local in time and work for generic dynamical gravitational systems.

Renormalizing the on-shell action variation offers two important advantages over renormalizing the action itself. First, the variation of the action has a universal form in which the bulk contribution vanishes identically. As a result, the renormalization problem is automatically localized at the boundary; no bulk subtractions are required. Second, the variation of the action admits a natural interpretation as a 1-form on functional space. The distinction between exact and non-exact 1-forms provides a clear renormalization prescription. We apply these ideas to the computation of on-shell black hole actions. After presenting the general algorithm, we discuss some examples, including Kerr-Newman, Kerr-Newman-AdS, Taub-NUT, Taub-Bolt, and STU black holes. We also apply the same techniques to the computation of holographic Wilson loops. All results agree with standard results, in particular with holographic renormalization.

Open systems are ubiquitous in physics. Many realistic systems interact, at least weakly, with environmental degrees of freedom that may be too numerous, too complicated, inaccessible, or unknown. When only a subset of degrees of freedom is observed, its reduced dynamics can differ qualitatively from that of a closed system, displaying dissipation, noise, decoherence, memory effects, or loss of information into unobserved sectors. When the microscopic description is also unknown, one is led to an open effective description, in which the relevant degrees of freedom are treated systematically while the environment and the microscopics are parametrized rather than solved for explicitly. This perspective is especially important in gravity and cosmology. The main open problems of cosmology, including inflation, dark matter, and dark energy, involve spacetime-filling sectors whose microscopic nature is unknown and whose observed effects are primarily gravitational. At the same time, gravitational systems often lack a preferred notion of conserved energy because they are time dependent, and naturally display out-of-equilibrium dynamics. These lecture notes introduce the operator formalism and the Schwinger-Keldysh path-integral as tools to study open systems, with emphasis on open effective field theories and inflation. They are aimed at master students, PhD students, and researchers approaching these topics for the first time.

Characterizations of the Gribov horizon have so far proceeded indirectly, through Zwanziger's horizon function or through Gribov's no-pole condition on the ghost propagator, each of which encodes the positivity of the Faddeev--Popov operator only approximately, whereas the construction developed here supplies a direct operator statement. Once the constant gauge modes are removed, the Landau-gauge Faddeev--Popov operator becomes congruent to a bounded, dimensionless operator assembled from the background field and the free Laplacian, so that the horizon condition reduces to an ordinary spectral threshold, attained when an eigenvalue of that operator crosses $-1$. Self-adjointness, ordinarily postulated as an independent hypothesis, follows in this formulation from Landau transversality alone, while the first-order character of the perturbation fixes an analytic scale distinct from the one governing the familiar Schrödinger problem. Because the ghost dressing function coincides with the diagonal resolvent of the same operator, Gribov's no-pole estimate emerges as its leading Born-order truncation, an identification that at once delimits the regime in which the estimate is trustworthy and the regime in which it fails. The construction is tested against an exact solution for a periodic transverse $SU(2)$ background, for which the threshold, its Born approximation, and the corrections beyond Born all admit closed forms, and for which the associated action and mode-counting entropy scale with the volume so that the two balance in four dimensions. The periodic family thereby furnishes a solvable reference case for the underlying mechanism, whereas extending the claim to generic Yang--Mills configurations constitutes a separate undertaking, whose requirements are stated explicitly.

Bosonic invertible and symmetry-protected topological (SPT) phases are well-known to be described by ordinary cohomology groups in low dimensions, but `beyond-cohomology' phases appear in higher dimensions. We make a systematic study of them, and find that the first major non-triviality is a mod-3 phenomenon, and not a mod-2 phenomenon as in the case of fermionic phases. We also point out that this is a dual manifestation of the classic question of Steenrod, namely the issue of the existence of homology cycles without manifold representatives. Thom developed the theory of cobordisms to answer this question, and we explain how the same analysis leads to Dijkgraaf-Witten phases which are nontrivial on general simplicial complexes but become trivial on manifolds.

We study cosmological collider signatures in a two-field inflationary system with constant-turn derivative mixing between the canonically normalized curvature fluctuation and a massive isocurvature field. Building on recently derived exact hypergeometric solutions that treat the quadratic mixing nonperturbatively, we construct the mixed propagators constituting the cosmological correlators. A Mellin-Barnes approach helps isolate the pair of nonanalytic late-time branches carried by a heavy field. For a cubic isocurvature self-interaction, these branches contribute towards a squeezed bispectrum with a power-law envelope and logarithmic oscillations. The oscillation frequency encodes the heavy mass, while the amplitude and phase retain the full mixing dependence rather than a perturbative expansion. We perform the squeezed limit integral analytically and compare it with numerical results across representative masses and mixing strengths. At fixed mixing we derive the large-mass JWKB expansion of the squeezed correlator and its phase. We also give integral representations for the isocurvature Wightman function. The research idea was suggested by ARC, the calculation was performed by GPT, and the results were checked by the authors.

An observer which propagates in a spacetime with dynamical gravity has access to an algebra of observables which is expected to be a von Neumann algebra with a trace. The observer can use projections from the algebra to perform local measurements. By using this fact we construct a simplicial complex out of measurements recorded on the worldline of the observer and we propose that such a complex captures topological information about spacetime, even when this is fluctuating.

We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.

Given a compact CY3 $Y$, its A-side (resp. B-side) universal intermediate Jacobian $X$ (resp. $X^{!}$) admits a natural hyperkahler structure. Both $X$ and $X^{!}$ determines 3d Rozansky-Witten theories, in both A-model and B-model. We describe some surprising 3d mirror symmetry phenomena between $X$ and $X^{!}$. This includes (i) a 3d SYZ construction of $X^{!}$ from $X$ via moduli of certain 3d A-branes in $X$ constructed from $D^{b}\left( Y,\Omega \right) $ with varying stability conditions given by $\varpi $; (ii) The 3d B-brane on $X^{!}$, constructed from varying $D^{b}\left( Y,\Omega \right) $ with fixed $\varpi $, is realized as the 3d SYZ transformation of a cotangent fiber 3d A-brane in $X$. Under mirror symmetry between $Y$ and $Y^{\vee }$, the roles for $X$ and $% X^{!}$ got interchanged. We also construct 3d A- and B-branes in $X$ and $X^{!}$ via DT theory and discrete symmetries on $Y$ and $Y^{\vee }$.

We propose a generalization of the defect extremal surface (DES) prescription to holographic interface conformal field theories (ICFTs), extending its applicability beyond the AdS$_3$/BCFT$_2$ framework. We consider a holographic ICFT$_2$ comprising two CFT$_2$s coupled across an interface, dual to two asymptotically AdS$_3$ geometries joined by a codimension-one end-of-the-world (EOW) brane. In the corresponding effective lower-dimensional description obtained via partial dimensional reduction on the brane-boundary combination, the theory on the brane is coupled to gravity, thereby enabling the computation of fine-grained entanglement entropy via the island formula. We demonstrate that the generalized DES prescription exactly reproduces the effective lower-dimensional results for finite subsystems in time-independent scenarios in the large brane tension limit, corresponding to weak gravitational coupling on the EOW brane. We further compute the entanglement entropy of semi-infinite bipartite pure states in radiation subsystems coupled to $2d$ eternal black holes, and obtain the corresponding Page curves.

We investigate the effects of excited normal modes on vortex dynamics in the Abelian Higgs model in the type I (static attraction) and type II (static repulsion) regimes. We demonstrate that shape normal modes compete with the static inter-vortex forces. This can result in excited type I (II) vortices repelling (attracting). In addition we observe the existence of spectral walls that prevent the formation (break up) of bound states in type I (II) systems. We study the long lived quasi-bound states and orbits induced by their competing forces and the effective centrifugal forces. Finally, we observe that the effect is strong enough to induce vortex-antivortex pairs to follow long-lived orbits.

In this work I study the effect of a magnetic field on the Casimir effect due to a massive, charged fermion field that violates Lorentz invariance in an aether-like manner while maintaining CPT, in a space with one toroidally compactified extra dimension. I take the fermion field to obey MIT bag boundary conditions on two identical square parallel plates. I do this investigation using the zeta function technique that enables me to calculate the Casimir energy and pressure in the presence of a constant magnetic field perpendicular to the plates. I examine the cases of timelike Lorentz violation, of spacelike Lorentz violation in the direction of the magnetic field, of spacelike Lorentz violation in the direction perpendicular to the magnetic field, and of spacelike Lorentz violation in the direction of the compactified extra dimension. In all scenarios, I find simple and accurate analytic expressions of the magnetic field dependent Casimir energy and pressure.

We study how the leading string-inspired quartic correction $\alpha'^2 F^4$ modifies holographic fermionic observables in a bottom-up $AdS_4/CFT_3$ model. The gauge sector is described by Maxwell electrodynamics supplemented by the quartic interaction, while the geometry is kept fixed in the probe approximation. We first analyze the nonlinear electrostatic background and derive an exact first integral of the gauge equation, the associated constitutive relation for the radial electric field, the critical coupling for globally regular solutions, and weak-coupling expansions for the electrostatic potential and chemical potential. We then use these backgrounds to compute the retarded Green's function and spectral function of charged probe fermions. The quartic interaction increases the chemical potential, lowers the effective ratio $T/\mu$, shifts the Fermi momentum, and enhances the spectral weight without destroying the holographic Fermi surface. We further show that the fermionic observables inherit the even-power dependence on $\alpha'$ implied by the analytic structure of the gauge sector. The resulting probe-limit analysis makes explicit how quartic bulk nonlinearities propagate from the bulk to boundary fermionic observables.

Using the effective field theory of multiple inflationary fluctuations, we present the first analytical calculation of the primordial bispectrum in which the quadratic mixing between curvature and isocurvature fluctuations is treated non-perturbatively. Building upon the operator representation of the exact linear solutions proposed in Ref.~\cite{Huenupi:2026abj}, we derive a simpler integral representation for these mixed mode functions. We prove that all scale-invariant tree-level bispectra reduce to a single vertex diagram, which can be evaluated with a Schwinger-parameter integral over independent pre-computable leg kernels. We showcase the power of our approach by considering the cubic time-derivative interaction $\dot{\pic}^3$, which leads to a purely single-field, equilateral phenomenology at small mixing. On the contrary, at strong mixing the obtained bispectrum shapes decorrelate from the equilateral template and become genuinely multifield, with a large amplitude, motivating a dedicated data analysis. The squeezed limit is obtained analytically in a closed form at any dimensionless mixing strength $\la$ for an isocurvature field of bare mass $m$ and features a cosmological collider signal set by $\nu_{\rm eff} = i \muf=\sqrt{9/4-m^2/H^2-\la^2}$, with an effective mass dressed by $\la$, as previously evidenced in numerical or semi-analytical calculations. Our results encompass the $\la \ll 1$ limit of usual perturbative calculations, where the amplitude of the signal is necessarily small, but they also surpass them, thus opening a new analytical window into large multifield primordial non-Gaussianities.

In the last decades, spacetime noncommutativity and the associated deformations of relativistic symmetries have attracted a lot of interest, as several phenomenological windows into quantum gravity are approaching genuine Planck-scale sensitivity. However, the physical significance of the mathematical structures introduced to deal with spacetime noncommutativity is still debated, and some crucial pieces are missing or poorly understood. From time to time it has been suggested that valuable insight into these conceptual challenges could come from the analysis of appropriately designed first-quantized toy models, in which major technical and interpretive issues can be effectively managed or sidestepped altogether. In this paper we take seriously this suggestion and develop the first fully consistent and fully relativistic first-quantized model of two particles propagating and interacting on a noncommutative spacetime. The specific spacetime noncommutativity implemented in our model, which we call 'time-commutative $\kappa$-plane', had already been proposed as a suitable arena for a first-quantized analysis, but previous studies were mostly heuristic and failed to provide a full description of the deformed relativistic symmetries. We here go much beyond those pioneering attempts: we find a full characterization of the appropriate deformed Poincaré symmetry algebra as well as its Galilean limit; we build a single-particle quantum model carrying an irreducible representation of the deformed Galilei algebra; we exhibit two consistent, Galilean-relativistic descriptions of a system of two quantum particles interacting via a deformed harmonic potential, finding that the structure of the two-particle symmetry generators is intimately connected with the deformation of the interaction law.

Cosmologically coupled black holes (CCBHs), whose masses evolve in response to the cosmological expansion, have recently attracted significant theoretical and observational interest. Existing studies have treated CCBHs as purely classical objects, neglecting the effect of Hawking radiation (HR), which competes with the cosmological coupling (CC) mechanism. We take a first step towards studying evaporating CCBHs, adopting a quasi-adiabatic approximation in which the HR rate is evaluated at the instantaneous CCBH mass, and modeling the CC mechanism through the phenomenological scaling of the mass with the scale factor, $M \propto a^k$. We show that, depending on the coupling strength $k$, even late-time CC activation can significantly delay Hawking evaporation, or lead to asymptotic CC-dominated mass growth, with important implications. We set limits on the abundance of primordial CCBHs from $\gamma$-ray observations, finding limits which are weaker than their uncoupled counterparts, as CCBHs are kept farther from the endpoint of evaporation for a longer time. Unlike standard primordial black holes, the CCBH formation and present-day masses no longer approximately coincide, even for formation masses $M_{\text{form}} \gtrsim 10^{15}\,{\text{g}}$. Therefore, the same population of primordial CCBHs may be subject to evaporation limits through its past emission history, as well as to other limits (such as microlensing) through its present-day mass.

We derive generalized effective Friedmann and Raychaudhuri equations for a bouncing polymer quantized Bianchi-I spacetime. We further prove that the relation numerically derived in the literature between the matter energy density and the anisotropic shear at the bounce holds exactly for any type of matter content, and derive explicit expressions for the constants that appear in that relation.

In this work, we have performed the theoretical estimation of the lowest boundary of an axion mass. We have analyzed the energy spectrum of the electron in a constant homogeneous magnetic field, taking into account its anomalous magnetic moment. We have applied the obtained results on the energy spectrum of the electron in a constant homogeneous magnetic field with allowance for its anomalous magnetic moment to the hydrogen atom electron, which is located in addition to the Coulomb field of the proton, as well as in the magnetic field produced by the magnetic moment of the proton. We have applied the idea of the restriction for the lowest boundary of the axion mass to the triplet-singlet transition between two adjacent levels obtained as a result of the hyperfine structure splitting of the s-levels in the hydrogen atom. We have concluded that the mass of an axion ought to be more than 5.885 microelectron-Volt. We have determined that the minimum value of the magnetic field strength at which the axion emission by the electron in a magnetic field starts to be realized is determined by the axion mass. This result enables us to estimate the expected value of the lowest boundary for the axion mass (of the order of 10 microelectron-Volt), assuming that some part of the solar axions is emitted by the electrons located in sunspots.

Atoms falling freely into a Bañados-Teitelboim-Zanelli (BTZ) black hole in a Boulware-like vacuum are shown to emit radiation with a Planck spectrum at the Hawking temperature $T_{H}$. This leads to thermal Hawking-like radiation for a cloud of falling atoms prepared with random initial times. Moreover, the radiation is related to the relative equivalence principle, with the vacuum field modes accelerated with respect to the falling atom. The physics of the atom-field interactions is most easily described within a quantum optics approach, where each atom can be interpreted as a detector. Despite the topological nature of gravity in $(2+1)$ dimensions, the thermodynamic and radiation properties of BTZ black holes are still universally governed by the same near-horizon conformal quantum mechanics (CQM) applicable to higher-dimensional gravity. This universal conformal behavior is exhibited by all fields in the background of generic black holes, and generates an HBAR entropy $S_{\mathcal P}$ associated with the photon radiation field that mimics the Bekenstein-Hawking entropy $S_{\mathrm{BH}}=A/4$, proportional to the black-hole horizon area, and with the correct $1/4$ proportionality factor.

Wide binary stars provide natural laboratories for directly probing gravity in the low-acceleration regime, as dark matter inferred from any viable gravity has negligible effects on their internal dynamics. Various recent studies including Bayesian 3D analyses have shown that wide binaries with separations greater than several thousand astronomical units experience MOND-type gravity with a boost factor of $\gamma\approx 1.3-1.6$. However, results claiming preference for, or no deviation from, standard gravity have also been published during the same period, particularly highlighting the roles of data quality control and realistic modeling of multiple-star (i.e., triple and higher-order) systems that host hidden companion stars. Here we carefully reexamine the issues of data quality control and modeling multiple-star systems in statistical gravity tests based on sky-projected 2D velocities of wide binary stars. Through extensive tests including the acceleration-plane test, the $\tilde v$-distribution test, and the median-$\tilde v$-profile test (where $\tilde v$ is the sky-plane 2D relative velocity normalized by the Newtonian circular velocity between the two stars), we show that proper data quality control or reasonable variation in multiple-star modeling cannot remove the low-acceleration gravitational anomaly but confirms the MOND-type gravitational anomaly, particularly consistent with recent realistic MOND solutions of wide binary orbits. We find that studies claiming no evidence for the low-acceleration gravitational anomaly are consequences of bypassed calibration of the fraction of multiple-star systems using the Newtonian-regime data, bias-introduction in data quality control that is not taken into account in gravity tests, or insufficient statistics in the low-acceleration regime.

We develop an analytic treatment of primordial non-Gaussianity in multifield inflation that is nonperturbative in the constant curvature--isocurvature mixing strength $\lambda$. Using exact linear solutions for the coupled curvature perturbation $\zeta$ and isocurvature perturbation $\sigma$, we construct dressed propagators and derive exact integral representations for the tree-level bispectra generated by the interactions $\dot\zeta^2\sigma$, $\dot\zeta\,\sigma^2$, and $\sigma^3$. This formalism resums curvature--isocurvature transfer to all orders in $\lambda$ and applies for arbitrary values of the entropy mass $\mu$. We obtain closed-form expressions for the leading squeezed limit of the bispectrum contributions and recover the well-known cosmological-collider and quasi-single-field results in the weak-mixing limit. In the strong-mixing regime, where conventional transfer perturbation theory breaks down, we find that both the power spectrum and the bispectrum can be dramatically enhanced, giving rise to distinctive nonperturbative scaling laws for the reduced non-Gaussian amplitude. Together, these results open a new analytic window onto multifield inflation beyond the weak-coupling approximation and establish a framework for studying cosmological-collider signals, primordial-black-hole production, and loop corrections in strongly mixed inflationary dynamics.

With generalized central binomial coefficients $ \binom{2x}{x}:=\frac{\Gamma(2x+1)}{[\Gamma(x+1)]^2}$ defined through Euler's gamma function, we represent deformed Apéry-like series \[ \mathscr A_{s,n}:=\sum_{k=1}^\infty\left.\!\frac{\partial^n}{\partial x^n}\frac{1}{x^s\binom{2x}{x}}\right|_{x=k} \] by multiple Clausen values (MCVs), which belong to a special class of cyclotomic multiple zeta values (CMZVs) at level $3$. For example, exploiting provable algebraic relations among MCVs, we show that \[\mathscr A_{1,5}=-\frac{9[495L(\chi_{-3},6)-30\pi^{2}L(\chi_{-3},4)-2\pi^{4}L(\chi_{-3},2)]}{4}\]and\[\mathscr A_{4,4}=\frac{352\zeta_{5,3}}{15}+\frac{752537\pi^{8}}{10206000},\]where $ L(\chi_{-3},s):=\sum_{n=0}^\infty\left[(3n+1)^{-s}-(3n+2)^{-s}\right]$ and $ \zeta_{5,3}:=\sum_{m=1}^\infty\sum_{n=1}^{m-1}m^{-5}n^{-3}$.

Bubble-wall friction controls the dynamics of first-order cosmological phase transitions. In Boltzmann-equation approaches, a major uncertainty arises from infrared gauge bosons, whose contribution is artificially enhanced in the massless approximation. We study the impact of thermal masses by including them consistently in both the Liouville operator and the collision integrals. Thermal masses suppress the source term for out-of-equilibrium perturbations while also reducing interaction rates. These effects largely cancel for top quarks, giving only percent-level changes, but they strongly suppress the infrared gauge-boson contribution, shifting the dominant momenta to scales of order the temperature. As a result, gauge bosons become subleading and wall velocities are close to those obtained from top-quark friction alone. We illustrate this in the singlet-extended Standard Model. Our results show that thermal masses reduce the sensitivity of friction calculations to the poorly controlled infrared sector of the plasma.

In a flat crystalline membrane, the low-energy spectrum is dominated by a flexural mode that does not couple to phonon Hall viscosity. We show that static curvature converts normal motion into in-plane strain and thereby opens a Hall-active flexural channel. Tracefree curvature couples directly to Hall-active shear, while mean curvature acts indirectly through the shear generated by ordinary in-plane elasticity. Together, these channels generate in-plane phonon angular momentum along the surface normal. For statistically isotropic shallow ripples, the time average has a definite sign fixed by the Hall viscosity, producing a steady field-odd torque proportional to the mean-square curvature. Using the measured bulk Hall viscosity of $\alpha$-RuCl$_3$ to set the scale, we estimate a torque of order $10^{-22}\,\mathrm{N\,m}$ for a few-layer membrane, within reach of demonstrated torsional sensors. The same flexural-to-shear response provides a probe of phonon Hall viscosity in atomically thin crystals.

We present a class of regular axisymmetric black hole geometries fully characterized by the parameters $\{{\cal M},a\}$ and possessing the Kerr event horizon. This family interpolates between regular spacetimes, configurations with integrable singularities, and the Kerr solution as a limiting case. Its main features are: (i) the existence of quasi-extremal configurations without requiring $a \approx {\cal M}$; and (ii) a possible framework toward an analytical description of Kerr black hole formation from an initially regular configuration.

In this work, we investigate a cross-section-ratio-based inversion method for extracting distribution functions at the Electron--Ion Collider (EIC). Starting from the general factorization formula $d\sigma = H \otimes f$, we show that, for an appropriate bremsstrahlung process and suitably chosen differential observables, the convolution structure can be reduced to a multiplicative form. On this basis, we define the ratio $R = \frac{d\sigma_{\mathrm{exp}}}{d\sigma_{\mathrm{hard}}},$ where $d\sigma_{\mathrm{exp}}$ is the experimentally measured differential cross section and $d\sigma_{\mathrm{hard}}$ is a perturbatively calculable theoretical input. We then establish the relation between $R$ and the target distribution function $f$. Finally, we investigate how the theoretical input $d\sigma_{\mathrm{hard}}$ should be constructed when soft-photon radiation, finite-bin-width effects, and experimental acceptance are taken into account.

We investigate dark matter (DM)-admixed neutron stars (NSs) within a self-consistent single-fluid relativistic mean-field framework by extending the Higgs-portal model with a massive $Z^\prime$ vector mediator. The resulting density-dependent repulsive interaction dynamically couples the baryonic matter (BM) and DM sectors, allowing the DM content to be characterized by the global particle fraction, $F_\chi=N_\chi/N_B$, with the local DM density determined self-consistently as $n_\chi=F_\chi n_B$, thereby eliminating the need for the externally prescribed DM Fermi momentum adopted in previous single-fluid models. Using the NL3$\omega\rho$, DD2, and FSU2R EOSs, we show that increasing $F_\chi$ systematically softens the nuclear equation of state (EOS), reduces the maximum NS mass by up to $\sim29\%$, increases stellar compactness, and modifies the thermodynamic response of dense matter. We further derive exact analytical expressions for the adiabatic speed of sound, its density derivative, and the adiabatic index, providing a rigorous benchmark for assessing the causality and thermodynamic stability of DM-admixed EOSs. At the microscopic level, the BM--DM interaction is shown to be dominated by the repulsive $Z^\prime$ vector channel. Our framework establishes a direct connection between collider-motivated WIMP models and the multimessenger phenomenology of NSs, with potential implications for future gravitational-wave and X-ray observations.

We study the spacelike-collinear limit of gauge-theory scattering amplitudes using the Method of Regions. The corresponding splitting amplitude violates strict collinear factorisation through its dependence on the non-collinear partons. While the associated colour dependence has long been known, starting at two loops the splitting amplitude also acquires dependence on their kinematics. We show that this kinematic dependence originates from a unique hidden region present in the asymptotic expansion of the five-point amplitude in the spacelike-collinear limit, but absent in the timelike limit. More generally, we propose that hidden regions provide the mechanism by which crossing-related asymptotic limits cease to be analytically connected. We develop a general algorithm for the systematic identification of hidden regions. Applying it to the five-point amplitude in super Yang-Mills theory, we compute the hidden-region contributions to the complete set of basis integrals and recover the exact kinematically dependent factorisation-violating splitting amplitude. In momentum space, the hidden region is characterised by soft and Glauber loop momenta. This explains why the Wilson-line calculation captures the complete kinematic dependence, thereby accounting for the observed universality across gauge theories.

Collinear splitting functions govern parton evolution, parton showers, and resummation at high-energy colliders. While on-shell spinor-helicity methods have successfully yielded massless QCD splitting functions, a complete on-shell construction for massive particles, systematically incorporating finite-mass effects, is less developed. We present an on-shell constructive formalism for massive collinear splitting functions based on Soper-Weinberg collinear spinors, whose transformation properties follow from a light-front Galilean subgroup of the Poincaré group. Decomposing massive momenta and spinors with respect to fixed lightlike vectors $n$ and $\bar n$ makes the expansion in the alignment regime $m<p_T\ll p_+$ manifest. The leading-order structures are matched to massless three-point amplitudes, while an additional Higgs momentum along $\bar n$ probes the subleading spinor components and relates them to massless four-point amplitudes. We derive the complete set of leading and subleading massive splitting functions for all Standard Model particles and establish a systematic matching dictionary between massless and massive coupling coefficients at both the three- and four-point levels. Higher-point splitting functions are obtained through the recursive bootstrap relation with a universal substitution rule as a consequence of the Galilean symmetry. This constructive framework extends naturally to effective field theory operators and higher perturbative orders, providing a flexible computational tool for precision collider physics and parton shower development.

Deep thermalisation characterises the emergence of universal quantum state ensembles on subsystems due to projective measurements on their complement. We study the notion of locality, or lack thereof, in this phenomenon by considering a subsystem partitioned into two disjoint subregions which remain causally disconnected at all times under unitary dynamics. We show that the onset of deep thermalisation in this geometry is fundamentally bounded by measurement-induced entanglement teleportation between the subregions. While measurements on the environment generate entanglement across the disconnected partitions -- suggesting an apparent non-locality -- we demonstrate that generic locally interacting systems exhibit an emergent locality. Specifically, the timescales for both deep thermalisation and entanglement teleportation scale logarithmically with the distance separating the subregions. Exceptions to this include special circuits where the randomness of the measurement outcomes is perfectly transmitted to the ensemble of states of the subsystem, conditioned on the outcomes; in such cases the timescale for deep thermalisation is finite leading to genuine non-locality.

Collisions of ultra-relativistic bubbles during cosmological phase transitions can produce particles much heavier than the transition scale. Previous analyses modelled this process as the off-shell decay of the scalar background. We show that its results parametrically overestimate hard particle production and depend on the gauge choice and the coordinate choice in field space. We propose an alternative formalism, analogous to the partonic description of high-energy collisions. In the ultra-relativistic limit, the colliding bubbles undergo nearly free passage and hard production arises from on-shell scatterings among the quanta constituting the Lorentz-contracted walls. We apply this approach to heavy scalar, fermion, and vector particle production, and study the implications for dark matter, leptogenesis, graviton production and primordial gravitational waves.

We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This phenomenon is known as symmetry fractionalization, and in general it signals the presence of certain discrete 't Hooft anomalies. We describe this in detail in the context of free Maxwell theory in four dimensions. This understanding allows us to deduce the 't Hooft anomalies of non-Abelian gauge theories with renormalization group flows into Maxwell theory by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We illustrate this method in $SU(2)$ gauge theories with matter fermions in diverse representations of the gauge group. For adjoint matter, we uncover a mixed anomaly involving the 0-form and 1-form symmetries, extending previous results. For $SU(2)$ QCD with fundamental fermions, the 't Hooft anomaly for the 0-form symmetries that is encoded by the fractionalization patterns of lines in the Maxwell phase is a consequence of the familiar perturbative (triangle) anomaly.

We revisit the chiral spectra on charged 1- and 5-branes in the 10d non-supersymmetric $\mathfrak{sp}(16)$ string theory (also known as the Sugimoto model), and verify that they consistently cancel the anomaly inflow induced by a Green--Schwarz mechanism in the bulk. By analyzing the $\mathfrak{sp}(16)$ representations arising from quantizing the fermion zero modes on these branes as well as uncharged 4-branes, we find compelling evidence that the global structure of the gauge group is $Sp(16)/\mathbb{Z}_2$. We further comment on a possible duality to non-supersymmetric heterotic strings, and explore bottom-up anomaly inflow constraints for 10d effective $Sp(16)/\mathbb{Z}_2$ gauge theories coupled to gravity.

We compute the partition function of the WZW model with target a compact Lie group $G$ by adapting a method used by Choi and Takhtajan to compute the heat kernel of the group manifold. The basic idea is to compute the partition function of a supersymmetric version of the WZW model using a form of supersymmetric localization and then use the fact that, since the fermions of the supersymmetric WZW model are actually decoupled from the bosons, this also determines the partition function of the purely bosonic WZW model. The result is a formula for the partition function as a sum over contributions from abelian classical solutions. We verify for $G=SU(2)$ that this formula agrees with the result for the same partition function that comes from the Weyl-Kac character formula. We extend the method of supersymmetric localization to certain related models such as the $SL(2,\mathbb{R})$ WZW model and a Wick-rotated version of this model in which the target space is hyperbolic three-space $H_3^+$.

We analyze the vacuum fluctuations and the stress-energy tensor of a scalar field of mass $M$ in a conical spacetime, where the topological singularity at the apex requires boundary conditions for the field equation. The necessity of boundary conditions was established by Kay and Studer in the early 1990s, while for $M=0$ stability is achieved only under Dirichlet boundary conditions, and for $M>q$ the field is stable and a localized mode emerges. This mode admits a natural interpretation as a covariant model of an extended particle detector, which allows us to investigate whahow such detectors modify the local vacuum structure. In this framework, the renormalized stress-energy tensor offers a natural way to quantify the influence of the detector on the surrounding spacetime.

We develop a localized particle detector model formulated as a massive quantum field on Minkowski spacetime with the spatial origin excised. To render the problem well posed at the puncture, we impose boundary conditions at the excised point, which we take to be of Robin type. This setup yields a discrete sector, given by bound state solutions of the radial equation with real, positive frequencies, which characterizes the detector. We construct the full two-point function and show its decomposition into (i) the discrete radial bound state sector, (ii) the boundary condition modified continuous sector, and (iii) the unmodified Dirichlet sector. We then compute the detector field's stress-energy tensor and prove its covariant conservation. For the specific localized modes in this setup, the discrete sector contribution cancels in the complete stress-energy tensor, leaving only boundary condition induced terms. Notably, the discrete modes crucial to localized field based detectors emerge naturally from the boundary conditions, without ad hoc confining potentials, providing a covariant framework that extends the traditional Unruh-DeWitt paradigm. This mechanism is not restricted to Minkowski spacetime; the same construction can be applied to massive fields on backgrounds with naked singularities, such as conical and global monopole spacetimes, offering a unified route to detector localization in a broad class of geometries.

We adapt the Hamilton-Jacobi method of holographic renormalization to scalar field theories in Minkowski spacetime with scattering boundary conditions. The approach yields a flat-space holographic dictionary in which the expectation value of a dual operator is given by the renormalized canonical momentum. The source of the operator is imposed as a Dirichlet condition in a radial timelike foliation of the bulk theory and corresponds to the scattering data appearing in the Arefeva-Faddeev-Slavnov generating functional. We initiate a study of massive scalars and interacting fields within this formalism and we comment on extensions to different bulk theories and backgrounds.

In this paper, we investigate the time evolution of entanglement entropy and mutual information for the spatially-infinite systems where we act with a primary operator on the vacuum state and then time-evolve it with the sequence of the Euclidean and Lorentzian time evolutions. Two-dimensional holographic conformal field theories describe the systems under consideration in this paper. The Euclidean time evolution is induced by the Rindler Hamiltonian and behaves as the regulator that tames the divergence induced by the local operator, while the Lorentzian one is induced by the uniform Hamiltonian. Under these time evolutions, we investigate the time ordering effect of the Rindler Euclidean and uniform Lorentzian time evolution operators. Consequently, we find the remarkable differences between those time evolutions are induced by whether those are unitary or non-unitary. Especially, we find that the unitary time evolution induces the late-time logarithmic growth of the entanglement entropy, while the non-unitary time evolution induces the late-time constant behavior. Furthermore, we investigate the dual gravity of the systems under consideration. Especially, we investigate the gravity duals of the systems with the insertion of the heavy primary operator and show that it is a black brane with a spacetime-dependent horizon.

In this note we initiate the study of ``twisted holography'' for the dualities involving the BFSS matrix quantum mechanics and the IKKT matrix model in their $N \rightarrow \infty$ limits. We identify the admissible twists of each model, compute their cohomology in the BV-BRST formalism, and identify them -- in the planar limit and in perturbation theory around the trivial background -- with corresponding twists of IIA and IIB string theories, respectively. The twisted gravitational duals make manifest certain infinite dimensional symmetry algebras. In the BFSS example, the dual IIA supergravity twists are also obtained as certain zero mode truncations of the minimal (1/16-BPS) and maximal (1/4-BPS) twists of eleven-dimensional supergravity.

The scattering amplitudes for colored scalars can be calculated using the so-called curve integral formula, relying on simple combinatorics. It introduces a set of global Schwinger parameters for all Feynman diagrams that contribute to an amplitude. We extend this construction to non-orientable surfaces by making use of the quasi-cluster algebras defined for non-orientable surfaces. We embed the non-orientable surface in a doubled orientable surface, and project the appropriate features onto the non-orientable surface. The curve integral formula can also be thought of as the high-tension limit of an appropriate string amplitude. As a check of our construction, we take a superstring amplitude with the Möbius strip topology and take its field theory limit to obtain the same Feynman diagrams as in the corresponding curve integral. Our construction can be generalized to arbitrary higher genus non-orientable surfaces. To illustrate this, we list the possible curves and their dual momenta for a two-loop non-orientable surface, and construct the surface Symanzik polynomials using the surface generalization of spanning trees.

By breaking dual conformal invariance, we transform cluster-algebraic predictions for the alphabet of 9-point amplitudes in $\mathcal{N}=4$ super Yang-Mills theory to analogous predictions for 5- and 6-point processes in QCD. We start by obtaining, for the first time, candidate letters for 6-point processes with one massive external leg, and discover that they surprisingly also contain nested square roots. We confirm that our results essentially contain the alphabet of all 1-loop integrals with these kinematics, and in their massless limit also the recently computed alphabet of finite, planar 2-loop amplitudes for 6-point massless QCD processes. In the latter case, we additionally find 162 letters that may appear at higher loops. We similarly produce candidate letters for 5-point 2-mass processes, whose comparison with the literature reveals a nontrivial overlap that also includes new letters.

We study the scalar perturbations of asymptotically flat extremal Reissner-Nordström black holes via the quantum Seiberg-Witten geometry of $\mathcal{N}=2$ SU(2) gauge theory with $N_f=2$ flavors. The radial master equation, governed by a double confluent Heun equation, is exactly mapped to the quantum Seiberg-Witten curve, providing an exact quantization condition derived from the non-perturbative Nekrasov-Shatashvili free energy. Analytically, this exact dictionary unveils precise gauge-theoretic interpretations for critical physical thresholds, demonstrating that the superradiance and mass decoupling limits naturally reduce the master equation to the Whittaker equation and the reduced doubly confluent Heun equation (the latter corresponds to the SW geometry of the $\mathcal{N}=2$ SU(2) gauge theory with $N_f=1$), respectively. At the strict extremal limit, the coalescence of horizons induces a topological singularity that complicates the spectral analysis. By accommodating this irregular singularity, our geometric framework resolves the singularity coalescence and enables the extraction of the discrete global quasinormal mode. As our main contribution, we provide the first non-perturbative evaluation of the quasinormal modes spectrum for simultaneously charged and massive scalar fields directly at strict extremity. Furthermore, our analytical results reproduce numerical benchmarks for both neutral and charged massless probes, and naturally capture quasi-resonance behaviors.

Supersymmetric sectors of $\mathcal{N}=4$ super-Yang-Mills theory motivate the study of the partition function for the counting of gauge-invariant functions of $d=2,3$ matrices transforming under the adjoint action of $U(N)$. The partition function $ \mathcal{Z}_d ( x) $ in the large $N$ limit has a known Hagedorn phase transition at $ x = d^{-1} $ which provides a simple model for the phase structure of the thermal partition function of SYM. We study the all-orders asymptotic expansion of $ \mathcal{Z}_d(x)$ based on a geometric picture of concentric circles of poles in the complex plane accumulating in a natural boundary at $|x| =1$. We find that the order by order structure has a precise combinatorial interpretation organized in terms of increasing cycle size of permutations arising in the enumeration of the invariants. We refer to this organization as small-cycle dominance, and find that it extends to refined versions of the partition functions depending on several complex variables. An analysis of the coefficients in the asymptotic expansion of $ \mathcal{Z}_d(x) $ using the modular property of the Dedekind eta function reveals that the asymptotic expansion is actually convergent for $d\ge d_{ \rm crit } = 13$. A fermionic version of $\mathcal{Z}_d (x)$ has an analogous critical dimension of $ d_{ \rm crit} = 7$. This distinction indicates that the partition functions of the matrix models can be completely reconstructed from their high-energy (UV) limit for $d\ge d_{ \rm crit}$ whereas additional input is required to reconstruct the exact coefficients of the low-energy (IR) expansion for $2\le d \le d_{ \rm crit } -1 $.

Gauge theories of massive $p$-forms are connected by various dualities, which hold classically but may be broken at the quantum level. One example is the $BF$ theory of topologically coupled $p$- and $(d-p-1)$-forms in $d$ dimensions, where the coupling between forms results in a manifestly gauge invariant mass term for either form when the other is integrated out classically. We perform the path integral quantisation of this theory; by integrating out one of the forms, the resulting determinants are sensitive to the topology of spacetime, and counterterms must be introduced to renormalise their divergences. We compute these determinants in terms of the topological numbers of spacetime, showing explicitly how the quantum duality of the massive theories is broken on topologically non-trivial backgrounds. This is directly related to the quantum breaking of the massless duality between the form that was integrated out and the longitudinal modes of its partner. In particular, the difference of counterterms is proportional to the Euler characteristic of spacetime. The existence of gravitational instantons suggests that these dualities may be broken even in Minkowski space in the presence of topological fluctuations.

We investigate the dynamical role of internal vibrational modes in the Abelian Higgs model, focusing on how Derrick-type excitations modify vortex dynamics and scattering processes. We study the scattering of excited vortices and show that the interplay between spectral flow and mode excitation generates effective forces and enables resonant energy transfer between translational and internal degrees of freedom. As a result, vortex dynamics become strongly non-adiabatic, exhibiting super-elastic collisions, oscillatory dependence of the final state on initial conditions, and the emergence of fractal structures in scattering diagrams. Our results demonstrate that internal vibrational modes play a fundamental role in vortex interactions, going beyond the standard moduli space approximation and revealing a rich phenomenology driven by mode dynamics.

We study three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Using an exact fluid/gravity correspondence, we derive a closed radial flow equation for the quasi-local stress tensor and show that it realizes the holographic $T\bar T$ deformation at finite cutoff. We further develop the inverse-scattering description of the boundary dynamics, identifying the gravitational interpretation of the associated spectral data and analyzing the finite-cutoff deformation of soliton solutions. Although the boundary evolution is governed by an integrable bi-Hamiltonian hierarchy, we show that the radial flow itself is not Hamiltonian with respect to the canonical Poisson structure. Our results establish a unified framework connecting integrability, quasi-local gravitational observables, inverse scattering, and finite-cutoff holography on non-compact boundaries.

We investigate Krylov spread complexity for states evolving under time-dependent Hamiltonians. For periodically driven systems, we formulate the problem within Floquet theory and show how the Magnus expansion provides a systematic approximation when the Floquet Hamiltonian is not available in closed form. We then extend this framework beyond periodic driving and demonstrate that, in addition to the globally truncated Magnus expansion, a piecewise Magnus expansion provides a reliable method when the global expansion loses convergence or accuracy. Our results provide practical tools for analyzing complexity growth in a broad class of time-dependent quantum systems.

We set up a bootstrap workflow to study four-point conformal integrals in position space, using leading singularities, single-valued multiple polylogarithmic ansätze and boundary data from expansion by regions. These four-point conformal integrals are general in the sense that they are generated by the four-point projections of all possible $f$-graphs, including all non-planar $f$-graph sectors. For three-loop cases, fourteen of the fifteen inequivalent integrand basis can be directly calculated by \texttt{HyperlogProcedures} and the last one is fixed by Gram identity. Then we concentrate on how far the bootstrap workflow can go for four-loop cases, though it works for three-loop cases as well. We show that integrals with several leading singularities can be made tractable by decomposing them into pieces with simpler cut structure. Some four-loop integrals which can not be calculated or very hard to be calculated by other methods for now are obtained in this way. We also provide a package with skill files which is suitable to be read and used by current AI models.

The {\Lambda}CDM model has long served as a robust and predictive framework for cosmology, successfully explaining a wide range of observations, including the accelerated expansion of the Universe. However, discrepancies in cosmological parameter estimates and recent findings, such as those from DESI, hint at potential deviations from {\Lambda}CDM. Gravitational wave (GW) observations offer an independent method to probe the nature of dark energy, leveraging GWs from compact binary mergers as standard candles. In this study, we demonstrate that the integrated GW memory over cosmological distances encodes a unique imprint of the background spacetime. Unlike previous analyses, our approach captures non-linear dependencies on cosmological quantities, resulting in an enhancement of the integrated GW memory by a factor of 100 for high-redshift sources well within the sensitivity range of next-generation detectors like Cosmic Explorer and the Einstein Telescope. We find that despite the diminishing strength of individual GWs at high redshifts, their cumulative effect leads to a significant amplification, akin to the integrated Sachs-Wolfe effect, offering a potential new avenue for cosmological studies. By examining a range of dark energy models, we reveal that GW memory is potentially highly sensitive to the underlying cosmological framework, making it a promising probe of dark energy. This novel approach presents the possibility of a fresh perspective to address persistent cosmological tensions, and the nature of dark energy.

We initiate the mathematical study of the boundary Carrollian conformal algebra (BCCA), an infinite-dimensional Lie algebra recently discovered in the context of Carrollian physics. The BCCA is an intriguing object from both physical and mathematical perspectives, since it is a filtered but not graded Lie algebra. In this paper, we first construct some modules for the BCCA and one of its subalgebras, which we call $\mathcal{O}$, by restriction of well-known modules of the BMS$_3$ and Witt algebras respectively. Along the way, we prove the irreducibility criteria for the so-called ``induced modules'' of the BMS$_3$ algebra (which we prefer to call massive modules to avoid ambiguity) and show that this is the same criteria for the irreducibility of the Verma modules of the BMS$_3$ algebra. Interestingly, the modules generated by the action of the BCCA on the generating vector of the massive modules are also irreducible under the same criteria. When this criteria holds, every massive module decomposes into a direct sum of two BCCA-submodules, each of which we conjecture to be indecomposable. Meanwhile, restricting Verma modules to the BCCA and $\mathcal{O}$ leads to free or ``almost free'' modules, which are not particularly interesting from a representation-theoretic viewpoint. This motivates the construction of BCCA modules intrinsically. To do this, we go through some structure theory on the BCCA to define a new basis and a decreasing filtration on the algebra, using which we construct Whittaker modules over the BCCA and the subalgebra $\mathcal{O}$ and prove criteria for their irreducibility.

Lattice simulations of two-color, two-flavor Quantum Chromodynamics (QCD) at finite quark chemical potential have revealed a distinctive peak structure in the sound velocity. Although chiral perturbation theory (ChPT) and the Nambu-Jona-Lasinio (NJL) model have been employed to explain this phenomenon, neither approach has fully captured the observed behavior. To address this discrepancy, we have extended the NJL framework by incorporating the Medium Separation Scheme (MSS). This approach isolates medium contributions from divergent integrals, allowing for a more accurate treatment of finite-density effects. Our results indicate a clear increase in the diquark gap ($\Delta$) with increasing chemical potential, consistent with what is also seen in perturbative QCD predictions at high densities. {}Furthermore, the MSS-modified NJL model successfully reproduces the observed peak in the sound velocity.

We present an improved subdominant-mode amplitude (SMA) test of general relativity (GR), which probes amplitude-level deviations in the higher-order modes of gravitational-wave (GW) signals from binary black hole mergers while keeping the dominant quadrupole mode fixed. Using a comprehensive parameter-estimation campaign, we benchmark the test against Gaussian noise fluctuations, waveform modeling systematics, and physical effects such as spin precession and orbital eccentricity. When applied to numerical-relativity simulations, the SMA test performs reliably for aligned-spin and mildly precessing systems but exhibits measurable biases for strongly precessing or eccentric binaries. Although designed to detect amplitude deviations, the test also responds coherently to phase perturbations, yielding apparent GR violations when applied to phase-modified waveforms. Applied to recent GW detections, we report the strongest constraint on the hexadecapolar $(4,4)$ mode amplitude deviation, $\delta A_{44} = -0.30^{+1.16}_{-3.45}$, consistent with GR. With these results, this work establishes the SMA test as a robust and broadly sensitive null test of general relativity and demonstrates a systematic approach for assessing the robustness of GW tests of GR.

We derive exact general solutions (as opposed to attractor particular solutions) for the evolution of a scalar field $\phi$ in a universe dominated by a background fluid with equation of state parameter $w_B = -1$, extending earlier work on exact solutions with $w_B > -1$. Straightfoward exact solutions exist when the evolution is described by a linear differential equation, corresponding to constant, linear, and quadratic potentials. In the nonlinear case, exact solutions are derived for $V = V_0\ln \phi$, $V = V_0 \phi^{1/2}$ and $V = V_0/\phi$, and the logarithmic potential also yields an exact first integral. These complicated parametric solutions are considerably less useful than those derived previously for a universe dominated by a barotropic fluid such as matter or radiation with $w_B > -1$. However, we generalize the slow-roll approximation and show that it applies to all sufficiently flat potentials in the case of a vacuum-dominated expansion, while it never applies when the universe is dominated by a background fluid with $w_B > -1$.

We study the motion of test particles around the Kerr--Bertotti--Robinson (KBR) black hole (BH) and explore how the three defining parameters, the mass $M$, rotation parameter $a$, and magnetic parameter $B$ influence their dynamics. We derive analytical expressions for the energy and angular momentum of stable equatorial circular orbits, along with the corresponding radial and latitudinal oscillation frequencies, as functions of $M$, $a$, and $B$. We also examine the key features of the quasi-periodic oscillations (QPOs) of test particles near stable circular orbits, including the precession effects such as periastron precession and the Lense-Thirring effect. We compare our results with those corresponding to the Kerr BH. We find that the particle motion is strongly shaped by the BH parameters. Using a WKB approach, we also study scalar quasinormal modes of rotating KBR BH in an external magnetic field and show that the magnetic field increases damping, while rotation and angular momentum mainly set the oscillation frequencies. Alternatively, general relativistic modeling of Bondi-Hoyle-Lyttleton (BHL) accretion onto rapidly rotating KBR BH shows that two distinct physical structures emerge and cyclically transform into one another over time. These processes produce either a strongly oscillating flip-flop shock cone or a nearly stationary toroidal structure, with their formation governed by the BH spin and magnetic curvature. Power spectral analysis shows that these configurations give rise to low- and high-frequency QPO, providing a unified theoretical framework to understand how multiple QPO-like features can arise in rapidly spinning accreting systems.

We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $\Psi$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $\langle \Psi^2 \rangle_{\textrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $\eta$ and retaining terms through $O(\eta^2)$, we find that $\langle \Psi^2 \rangle_{\textrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result--with the event horizon radius modified by the presence of $\eta$. We also investigate whether an analogous decomposition holds for $\langle T^{\mu}_{\phantom{\mu}\mu}\rangle_\textrm{ren}$ when it is determined by this method. Our result parallels earlier analyses of Schwarzschild black holes pierced by a cosmic string.

We investigate a class of first-order scalar field theories minimally coupled to a Carrollian connection that are defined intrinsically on the Carrollian plane, i.e., the theories are not defined via limits of Lorentzian theories. The theories built are invariant under the extended Carrollian transformations which include supertranslations. The symmetry allows for a large class of Lagrangians, independence of spacetime coordinates is all that is required. However, invariance under supertranslations (which include boosts as linear supertranslations) forces the energy density to be static and the momentum density to vanish -- this precludes on-shell propagation of fields. Thus, to have propagating theories, one must move beyond single field theories that are minimally coupled to the geometry.

One of the main features of nonlinear electrodynamics is the existence of an effective geometry that describes the geodesic motion of photons. A detailed analysis of the properties of effective geometry is of utmost importance for a better understanding of nonlinear electrodynamics theories and their possible imprints on physics, especially in the context of black holes. We consider a nonlinear electrodynamics model that depends on the two electromagnetic scalar invariants and obtain that the motion of photons in nonlinear electrodynamics exhibits \textit{vacuum birefringence}, i.e., photons can propagate along two distinct paths, depending on their polarization. As a consequence of this phenomenon, we show that static black hole solutions sourced by nonlinear electrodynamics can admit two distinct unstable light rings, leading to the formation of two distinct shadows. Moreover, to explore the potential astrophysical relevance of our results, we also compare them with the astrophysical observations for the shadow radius of Sagittarius A*. We place upper limits on the charge-to-mass ratio of the nonlinear electrodynamics-sourced black hole. We also show that the motion of photons in this context can be interpreted as nongeodesic curves subjected to a four-force term from the perspective of an observer in the spacetime metric, generalizing previous results in the literature for nonlinear electrodynamics models that depend on a single electromagnetic scalar invariant.

We study the impact of radiation on quantum systems defined by the spins of elementary fermion-antifermion pairs produced at colliders. We present predictions for several processes, showing that energetic final-state radiation can induce decoherence and significantly reduce the entanglement of quantum systems formed by elementary fermion pairs. We investigate the feasibility of observing this effect experimentally in exclusive samples with energetic radiation. A statistically significant signal can be obtained with current data in associated $pp \rightarrow t\bar{t}(g)$ production at the LHC and in $e^+e^- \rightarrow \tau^{+}\tau^{-}(\gamma)$ production at Belle 2. Future electron-positron colliders operated at the $Z$ pole or well above the $t\bar{t}$ production threshold will extend these prospects further.

At a quantum critical point, the universal scaling behavior of Rényi entanglement entropy is controlled by the universality class of the codimension-two Rényi (or conical) defects in the infrared theory. In this work we perform a systematic study of critical correlations along Rényi defect lines in (2+1)d quantum spin models realizing quantum phase transitions described by the O(3) Wilson-Fisher universality class, using large-scale quantum Monte Carlo simulations. We present numerical evidence that, for a fixed Rényi index $n$, there exist multiple Rényi defect universality classes, with distinct critical exponents for the O(3) order parameter on the defect. These universality classes are realized by choosing microscopically different entanglement cuts in lattice models, which we classify as ordinary, special and extraordinary according to their relation to surface criticality. For the extraordinary entanglement cut, we further find evidence for a phase transition on the defect as a function of the Rényi index. Our results highlight the key role of defect universality classes in determining the universal scaling of Rényi entropy, and provide a framework for understanding the previously observed dependence of Rényi entropy scaling on microscopic lattice details.

Current observations constrain primordial perturbations to be adiabatic, approximately Gaussian, and nearly-scale invariant. However, a generic mixed state satisfying these constraints has additional unconstrained degrees of freedom, which can be parameterized by the purity of the state and its momentum variance. This allowable parameter space reveals a unified geometric landscape of mixed states, allowing us to map and relate distinct models of decoherence and their respective pointer bases. Within this landscape we show that decoherence models that "classicalize" -- in the sense of admitting a regular, positive-definite Glauber-Sudarshan $P$-function -- must actively inject momentum into the system, exceeding that of the vacuum. The enhanced momentum sources the decaying mode of the curvature perturbation, backreacting on the Newtonian potential and radiation-era geometry. While this mode decays away fast enough to preserve the temporal coherence of the CMB acoustic peaks, requiring the potential to remain within linear perturbation theory places a model-independent bound on the momentum variance generated by any model of decoherence. This bound is definitively violated by decohered thermal states with more than $14$ e-folds of inflation, while a strong dependence on the number of e-folds restricts amplitude-basis decoherence to fewer than roughly $64$ e-folds of inflation in order to stay in the linear regime. Altogether, we present a unifying framework for evaluating the quantum-to-classical transition of the early universe.

Recent baryon acoustic oscillation measurements from DESI provide important new clues for reassessing whether the standard $\Lambda$CDM model offers a sufficient description of the late-time expansion history of the Universe. When combined with cosmic microwave background and type Ia supernova data, these measurements show an apparent departure from the $\Lambda$CDM model, commonly described as dynamical dark energy (DDE) with equation of state crossing the phantom divide (i.e., quintom behavior). This review examines the current status of the DESI-motivated indications for DDE and their possible implications for physics beyond $\Lambda$CDM. We discuss how the strength of the preference for DDE depends on the adopted parametrization and dataset combination, and how residual systematics or internal tensions among datasets may affect its interpretation. At the background level, several mechanisms beyond $\Lambda$CDM can produce similar expansion histories. We therefore further discuss how the same effective departure from $w=-1$ may arise from physically distinct scenarios, including interacting dark energy, non-minimally coupled gravity, and non-standard dark matter. Meanwhile, these different new-physics interpretations may have different implications for current cosmological tensions, especially those involving $H_0$, $S_8$, and $\sum m_\nu$. In conclusion, the question posed by DESI is not merely whether dark energy evolves with time, but rather how, within the framework of precision cosmology, to disentangle new physics scenarios from systematic errors.