Papers

We show that, for stationary geometries whose linearized fluctuation equations separate into radial and angular Heun equations, a pair of diffeomorphisms projects the full problem onto two coupled, isospectral Gauss hypergeometric problems in complementary spacetime regions. This projection requires Robin boundary conditions to be imposed at the intersection between the complementary regions, which are uniquely fixed by requiring the two diffeomorphisms to match there. The method provides an independent derivation of recent results obtained from the correspondence between Heun connection coefficients and instanton partition functions in the Nekrasov-Shatashvili limit. As an application, we identify a subset of modes in Kerr-de Sitter and Kerr-anti-de Sitter black holes that, in the near-extremal limit, continuously reduce to a basis of the Schwarzian/Jackiw-Teitelboim functional space of gravitational fluctuations.

Information distance and circuit complexity are both obtained by minimizing lengths, but they minimize over different objects. We make this distinction explicit for faithful one-mode Gaussian states. First, invariant-form uniqueness implies that no positive-definite quadratic gate cost can be invariant under the full adjoint action of the noncompact symplectic group; a positive Cartan majorant necessarily introduces additional reference data. The Uhlmann purification quotient realizes the Bures metric, and the radial covariance direction requires a system-ancilla coupling because system-only Gaussian unitaries preserve the Williamson eigenvalue. We then minimize fixed right-invariant quadratic norms on the minimal two-mode Gaussian gate algebra \(\mathfrak{sp}(4,\mathbb R)\). For the unweighted Frobenius norm, the quotient coefficients for radial and traceless covariance tangents are $G_0=[\hbar^2(u-1)]^{-1}$ and $G_2=[\hbar^2(3u-1)]^{-1}$, where $u=(2\nu/\hbar)^2$. Their ratio does not equal the Bures ratio. The radial coefficient, however, reproduces the Bures value exactly at every $u$; the mismatch is confined to the traceless sector. More generally, a constant block-diagonal two-weight schedule gives $G_0/G_2=1+2(\beta/\alpha)u/(u-1)$; matching Bures throughout the isotropic family would require the state-dependent relation $\beta/\alpha=1/u$. At the Bures-Fisher determinant crossing \(u=\varphi\), pointwise matching is possible only by inserting $\beta/\alpha=\varphi^{-1}$. Thus the Bures purification quotient is an exact state-geometric cost, but it is neither an unweighted symplectic gate cost nor a member of this fixed two-weight Nielsen family. The existence of a more general fixed positive gate norm realizing the quotient remains open.

A precise characterization of the QCD phase transition remains a fundamental open problem, primarily due to the intrinsically non-perturbative nature of the dynamics that govern the breakdown of We quantify the logarithmic thermal variation of the normalized enthalpy density in finite-temperature Quantum Chromodynamics using a dimensionless response thermal function, $\mathcal{H}(T)$. We establish an exact identity that links $\mathcal{H}(T)$ to the speed of sound, $c_s^2(T)$. Using continuum-extrapolated lattice Quantum Chromodynamics, Monte Carlo uncertainty propagation, and cubic spline interpolation, we extract a stable peak at $T_{\text{peak}} \approx 153.6\text{ MeV}$ ($\mathcal{H}_{\text{peak}} \approx 6.24$), which remains robust under changes in the smoothing parameter $s$. By contrast, $\mathcal{H}(T) = 0$ for the MIT Bag Model despite its non-vanishing trace anomaly. We highlight $\mathcal{H}(T)$ as an effective diagnostic of the QCD crossover and discuss its limitations for universal critical scaling at zero chemical potential.

Parton distribution functions (PDFs) provide one of the most direct ways to describe the partonic structure of hadrons in QCD. They encode nonperturbative information about quarks, antiquarks, and gluons as functions of the partonic momentum fraction $x$, and they connect this microscopic structure to experimentally measurable high-energy scattering processes through QCD factorization. This makes PDFs interesting to pursue with lattice QCD, which provides a first-principles formulation of the strong interaction. The challenge is that PDFs are defined through light-cone correlations, while lattice QCD is formulated in Euclidean spacetime. This chapter introduces the theoretical foundations and current status of lattice-QCD calculations of PDFs, with emphasis on modern approaches based on spatially nonlocal matrix elements. We first review the light-cone definitions of quark and gluon PDFs, their Mellin moments, and the connection to QCD factorization. We then explain how large-momentum effective theory, short-distance factorization, and the short-distance operator product expansion make it possible to relate Euclidean lattice observables to light-cone partonic structure. Particular attention is given to the elements that have improved over the last five years: renormalization of Wilson-line operators, perturbative matching, finite-momentum and finite-distance effects, reconstruction of the $x$ dependence, and systematic uncertainties. We summarize selected lattice results for proton quark PDFs, pion and kaon PDFs, gluon PDFs, and twist-3 distributions, highlighting both recent progress and remaining challenges. As will be demonstrated, lattice QCD is moving from proof-of-principle calculations toward systematically improvable determinations that can complement experimental data and global QCD analyses in mapping the partonic structure of hadrons.

It is well known that the inclusive cross section in QED is infrared finite. In the standard diagram techniques this result follows from cancellation of infrared divergences. We suggest a new approach that should lead to IR -safe computational technique for QED with massive fermions.

Among three-dimensional massive gravities, Minimal Massive Gravity (MMG) is distinguished by a parameter regime in which the AdS bulk theory and the dual conformal field theory can be simultaneously unitary. We couple MMG to a finite tower of higher-spins by promoting the fields of its first-order formulation to $\mathfrak{sl}(N)$-valued ones. We also present an extended formulation involving a group-valued Stückelberg scalar, which realizes the higher-spin translations broken by the massive deformation. We then construct AdS$_2\times$S$^1$ solutions carrying higher-spin hair specific to the massive theory. Finally, we analyse the mass spectrum of the higher-spin modes around AdS$_3$.

We study dynamical effects during nucleation in thermal first-order phase transitions in field theory. Focusing on the classical regime of the decay of a metastable state, we present the general formula for the thermal decay rate including the dynamical prefactor and give a recipe for its systematic evaluation. We describe the physical mechanism which reduces the actual thermal decay rate with respect to the statistical rate obtained in equilibrium theory. We also discuss the thermality conditions ensuring the existence of a steady-state thermal rate, in which case our formula is exact up to exponentially small corrections. We show that it reproduces the known results for the nucleation rate in stochastic mechanics and field theory, and allows us to unify and go beyond them. We illustrate this in real-time numerical simulations of simple field theory models. We observe significant non-perturbative contributions which can dominate the dynamical prefactor in weakly-coupled field theories at moderate exponential suppression of the decay rate. We explore the connection of these non-perturbative effects to oscillons. Notably, our numerical method requires exponentially less computing time than direct simulations of decays and is thus applicable to systems with arbitrarily strong exponential suppression. Finally, we discuss small or poorly thermalized systems when the thermality conditions are violated and the steady-state rate does not exist.

We study the flavour structure of an $SU(15)_p$ confining chiral gauge theory in which the Standard Model (SM) quarks, leptons, and Higgs emerge as composite bound states. The couplings of two scalar fields in the conjugate antisymmetric ($\overline{\mathbf{105}}$) and conjugate symmetric ($\overline{\mathbf{120}}$) representations of $SU(15)_p$ provide two $SU(4)_F$ flavour-breaking spurions that generate both the SM Yukawa couplings and the flavour-changing processes. The up and down Yukawa matrices are tightly-correlated due to a "right-handed isospin" symmetry, which predicts a trivial CKM matrix in the absence of spontaneous symmetry breaking. The lepton Yukawas are correlated with the quarks due to a common source of flavour spurions. With a judicious Froggatt-Nielsen-like texture for the two flavour spurions we find that a benchmark fit with $\mathcal{O}(1)$ non-perturbative coefficients reproduces all six quark masses, three charged lepton masses, and the CKM matrix. The same spurions mediate charged lepton flavour violation, neutral meson mixing, rare kaon decays, and induce electric dipole moments. We compare the reach on the compositeness scale $\Lambda_{\rm pre}$ across these observables in the numerical benchmark and find that the electron EDM and $K^0$-$\bar{K}^0$ mixing provide the strongest sensitivity, reaching $\mathcal{O}(10^4)$ TeV, the lower end of the range probed by proton decay, while $\mu\to e\gamma$, $D^0$-$\bar{D}^0$ mixing, and $\mu$-$e$ conversion give complementary reach at $10^2$-$10^3$ TeV. The projected electron EDM sensitivity extends this to $\mathcal{O}(10^6)$ TeV, beyond the reach of planned proton decay searches.

It has previously been shown by Rajput, Roggero, and Wiebe that $\mathbb Z_2$ Gauss's law constraints can be used to build efficient quantum error-correcting codes (QECCs) that are robust against arbitrary single-qubit errors. In this work, we generalize the construction to be robust against arbitrary $t$-qubit errors, where $t$ is any positive integer. This includes a derivation of the optimal Gauss's law code within the considered family by minimizing the number of physical qubits required for a given code distance. Finally, we compare our codes against other efficient QECCs on metrics such as the number of physical qubits, the locality of the encoded Hamiltonian, and the logical error rate in the code capacity setting. Compared to using a domain-agnostic code for every lattice degree of freedom, we find that the Gauss's law code primarily excels at reducing the locality of the encoded Hamiltonian. Moreover, the physical qubit overhead is also reduced for $t \le 3$ (distance $d \le 7$).

It is widely believed that Coleman–De Luccia (CDL) instantons characterize tunneling transitions in a de Sitter multiverse. Their most naive interpretation uses analytic continuation to Lorentzian de Sitter at the minimal size of the spatial three-sphere. However, what one really wants is a geometry where a small bubble of new vacuum forms within the huge spatial sphere of an old parent de Sitter. Even by applying de Sitter isometries to the original CDL solutions, this cannot in general be achieved. In particular, it fails in the gravity-dominated regime, i.e. for up-tunneling and for transitions with heavy domain walls. These cases remain pathological in that the whole multiverse is in the causal future of every single up-tunneling event. To solve this problem, we develop a Hamiltonian description of how a small off-shell bubble grows and eventually goes on shell within the large spatial sphere of late-time de Sitter. We provide the corresponding WKB analysis, recovering the CDL rate. We explain that our tunneling process and that of CDL are described by two different analytic continuations of a unique on-shell trajectory in the Hamiltonian treatment. Our analysis has crucial implications for the Larfors–Johnson problem, which questions the standard mechanism for populating the string-theoretic flux landscape on the basis of an instability of the relevant domain walls.

Compact objects with the same exterior metric are locally indistinguishable to test particles, yet observables built from retarded fields can retain information about the spacetime outside the particle's immediate neighbourhood. The self-force acting on a particle in curved spacetime provides a unique probe of both the local geometry and the global structure of the background spacetime. We calculate the static, conservative self-force on minimally coupled scalar and electric charges in the simplest thin-shell gravastar: a de Sitter core matched to a Schwarzschild exterior. Weak-field expansions in the compactness $M/R$ are obtained analytically and summed in closed form. For a scalar charge outside the gravastar the self-force is nonzero—in contrast to the exactly vanishing result for a Schwarzschild black hole of the same mass—and behaves as $\tfrac{2}{5}q^2 M R^2/r_0^5$ at large distances, while for an electric charge the universal Smith–Will force $e^2M/r_0^3$ is corrected by a structure-dependent term $\tfrac{4}{5}e^2 M R^2/r_0^5$. Inside the gravastar the scalar self-force is directed toward the center at leading order in $M/R$, vanishes linearly at the center, and produces harmonic oscillations of the charge about the center; the electromagnetic self-force inside the gravastar behaves similarly. The results demonstrate explicitly that the self-force depends not only on the local curvature surrounding the particle but also on the global structure of spacetime: although the exterior geometry of a gravastar is identical to that of a Schwarzschild black hole, the interior boundary conditions modify the regular field and therefore produce distinct self-forces.

In this paper, we apply the covariant phase space formalism to the perturbative canonical quantization of the Pais-Uhlenbeck oscillator, with the acceleration-squared term treated as a perturbation. We quantize this model by constructing the symplectic form on the low-energy solution space. We then compute the energy spectrum and the unequal-time commutator in a perturbative way, and obtain the results that agree with the expansion of the exact low-energy theory. The perturbation method bypasses the standard Ostrogradsky construction and naturally decouples the Ostrogradsky ghost. This work extends our previous perturbative quantization scheme to genuine higher-derivative theories.

We study the differential Poisson sigma model (DPSM) in the symplectic case and show that its classical reduction defines a distinguished class of A-type models on symplectic targets, not necessarily Kähler. The DPSM is a covariant first-order sigma model whose graded target is the parity-shifted tangent bundle $T[1]M$ of a Poisson manifold $M$. Its graded Poisson tensor encodes a differential Poisson bracket on $C(T[1]M)\cong\Omega^\bullet(M)$, written covariantly in terms of a connection $\Gamma$ and its transpose $\widetilde\Gamma$. In the nondegenerate case, the Jacobi identities force $\Gamma$ to be flat, while the quartic coupling of the reduced action is given by the curvature of $\widetilde\Gamma$, induced by the torsion of $\Gamma$. Thus, the DPSM selects a symplectic class in which the A-model curvature coupling acquires a first-order Poisson origin. We describe this class through examples and obstructions; $\mathbb{CP}^n$ and K3 surfaces are excluded, while affine symplectic targets, symplectic tori, and the Kodaira–Thurston manifold furnish explicit examples. The graded parent geometry on $T[1]M$ equips $\Omega^\bullet(M)$ with a differential graded Poisson algebra structure; in particular, the underlying differential graded Lie algebra defines a strict $L_\infty$-algebra on the observable complex. This chain-level structure is not manifest in the usual Kähler formulation of the A-model.

We investigate the recent proposal of holographic volume complexity for timelike subregions \cite{Alishahiha:2025xml} in the framework of static patch holography for de Sitter spacetime. Using the stretched-horizon prescription, we compute the timelike subregion complexity as a function of the subregion duration for pure de Sitter and Schwarzschild de Sitter geometries. In pure de Sitter spacetime, the timelike subregion complexity displays exponential growth for short durations, and hyperfast growth near a maximal duration, paralleling the features of spacelike volume complexity \cite{Jorstad:2022mls}. For Schwarzschild de Sitter, when the stretched horizon is near the cosmological horizon, the behavior broadly remains similar to pure de Sitter. However, when the stretched horizon is near the black hole horizon, the hyperfast growth for long durations is replaced by nonlinear growth regime. Along the way, we also compute the corresponding timelike holographic entanglement entropy for de Sitter and Schwarzschild de Sitter.

Quantum integrability is a cornerstone of the exact theory of interacting quantum spin chains. In its standard formulation, however, one starts from R-matrices satisfying the Yang–Baxter equation, rather than from the Hamiltonian itself. It has therefore remained unclear how Yang–Baxter solvability can be characterized directly at the Hamiltonian level, and how it is related to the existence of local conservation laws. Here we prove that, in a broad standard setting, the Reshetikhin condition is not only necessary but also sufficient for Yang–Baxter integrability, thereby reducing the hidden algebraic structure of integrability to a Hamiltonian-level conservation law. Since the Reshetikhin condition is equivalent to conservation of the total energy current, this Hamiltonian-level criterion is also experimentally accessible. This result establishes a quantum counterpart of the Liouville–Arnold theorem for isotropic spin chains, stating that Yang–Baxter solvability is equivalent to an infinite hierarchy of local conserved quantities. Our result also simplifies substantially the search for integrable spin chains by replacing the search for R-matrices with a direct criterion on local Hamiltonians.

We obtain a tensionless limit of the M-theory 5-brane action and discuss its properties. The consistency of this limit requires that the field strength $H_3$ of the 2-form gauge field on the M5 brane worldvolume is non-vanishing and non-degenerate, so that one can also regard it as a strong $H_3$-field limit. The induced $6d$ worldvolume metric of this theory is non-degenerate in contrast to conventional tensionless (null) $p$-branes. We find that the tensionless M5-brane action is invariant under a super-Weyl symmetry acting on the bulk supergeometry, while in the purely bosonic case the action is invariant under an 11D target-space conformal symmetry, a property which is characteristic for the tensionless bosonic branes. Upon imposing a static gauge, which fixes worldvolume diffeomorphisms, this 11D conformal symmetry becomes a deformed 6d worldvolume conformal symmetry whose action on the worldvolume coordinates involves field dependent terms. When the transversal fluctuations of the 5-brane in the bulk are zero, the model reduces to the conformal non-linear chiral 2-form electrodynamics considered earlier by Gibbons and West, and by Townsend.

We propose a holographic map from the semiclassical Hilbert space of pure general relativity in $\text{AdS}_{3}$ to that of $\text{CFT}_{2}$. We define the bulk Hilbert space by semiclassically quantising the phase space in the basis of a fixed-area network on a Cauchy slice $\Sigma$. A fixed-area network is a maximal non-intersecting set of geodesics on $\Sigma$ whose lengths and angular momenta have been fixed. Our holographic map differentiates between `external' geodesics that are homotopic to a connected component of $\partial \Sigma$, and `internal' geodesics which are not. The lengths and angular momenta of external geodesics become conformal weights of primaries in the Hilbert space of the CFT living on the corresponding component of $\partial \Sigma$. The fixed-area network determines the wave function, which is given by a network of OPE coefficients of primaries whose weights are determined by the corresponding lengths. For sufficiently semiclassical states, there is an agreement between bulk and boundary inner products. We apply this proposal to various physics questions. The boundary dual of a bulk gauge turns out to be an emergent basis for sufficiently semiclassical states. We also define boundary operators that measure the lengths of geodesics behind the horizon, again in semiclassical states. Finally, we apply our map to closed universes and find a failure of semiclassicality in simple cases, which can be partially alleviated by the addition of a massive probe.

This chapter gives an overview of the recent progress in extracting generalized parton distributions from lattice QCD. We briefly recall the theoretical principles of GPDs and explain the two most common lattice approaches, Ji's quasi-distributions and Radyushkin's pseudo-distributions. In the second part of the chapter, we review the lattice results obtained from these two frameworks. Finally, we offer a discussion of future prospects of lattice extractions of GPDs.

We construct an explicit model where dark matter consists of 't Hooft-Polyakov monopoles. The dark sector is in thermal contact with the Standard Model, and dark monopoles are created by a thermal phase transition in the early Universe. Generically, the abundance of monopoles is negligible with respect to that of stable dark elementary particles. We show how to avoid this by taking the lightest stable particle, a dark fermion, sufficiently light for its abundance to be suppressed, yet heavy enough to satisfy constraints on dark radiation. In this specific window of parameters, dark matter is composed of monopoles with a mass of about $10^8$ GeV or larger, depending on the nature of the phase transition. This candidate lies beyond the reach of present, conventional dark-matter detection experiments. However, the model necessarily predicts dark radiation, with $\Delta N_{\rm eff}$ close to present-day bounds. In addition, if the dark phase transition is strongly first order, we find that the corresponding gravitational wave spectrum lies close to the region probed by future interferometers.

We apply topological vertex techniques to Calabi-Yau threefolds dual to brane webs where several 5-branes can end on the same 7-brane. In this context, we determine how topological string partition functions transform under Hanany-Witten transitions and flops, which allows us to track curves and the associated invariants under such transitions. The contributions of parallel external branes form a universal sector invisible to the 5d SCFT; once it is removed, invariants can be transported between different geometries engineering the same theory. This yields an efficient technique to compute Gopakumar-Vafa invariants at any degree and genus. We illustrate this with local Hirzebruch and del Pezzo surfaces, including $dP_4$, whose invariants we obtain at high degree for the first time.

We study how much of the proto-area response can be inferred from the bulk von Neumann entropy. In the perturbative holographic code setting considered by CCKLP and Witten, we keep the recovery frame fixed and analyze the response averaged over the GUE at second order in the encoding perturbation. Near the maximally mixed bulk spectrum, the response is fixed by the entropy through quadratic order. For $d_1\geq3$, spectral information first enters at cubic order through the third centered moment, so states with the same entropy can have different responses. We determine the resulting response range on small equal-entropy level sets and obtain its sharp leading $D^{3/2}$ dependence, including the coefficient. The corresponding minimax error for prediction from entropy alone is one half of this range. For $d_1=2$, the entropy instead determines the response exactly.

The entanglement entropy of quantum systems typically exhibits both ultraviolet and infrared (IR) divergences. In the low-frequency limit, the IR divergence is intimately tied to the unbounded spatial delocalization of zero-modes, a pathological feature common to both coupled harmonic oscillators and massless scalar fields. In this work, we demonstrate that this infinite growth is naturally resolved by invoking the Extended Uncertainty Principle (EUP), which introduces large-length-scale geometric corrections to the canonical commutation relations. By exactly solving the simple harmonic oscillator under the EUP framework, we establish the existence of an intrinsic geometric confinement that enforces a strict upper bound on the position variance, limits spatial delocalization, and introduces an intrinsic localization length scale related to the background Ricci scalar. We extend this regularizing mechanism to many-body systems by evaluating the entanglement entropy and entanglement spectrum of a one-dimensional harmonic chain and a massless scalar field. We show that the EUP-induced spatial bounds prevent the accumulation of low-lying long-wavelength modes, keeping the entanglement spectrum discrete and evenly gapped even in the strictly massless limit. This non-vanishing modular gap effectively caps the local entanglement temperature of the vacuum. Consequently, the entanglement entropy saturates to a finite value, providing a robust, geometric resolution to the zero-mode IR divergence problem in quantum field theory.

In this paper we investigate an entanglement measure, the Rényi entropy, in a 1+1D integrable quantum field theory known as the Federbush model. This is a deformation of the theory of two massive Dirac fermions by means of a bilinear term in the $U(1)$ currents that couples the two fermion species. This deformation gives rise to $S$-matrix elements which are coupling-dependent phases, distinct from $- 1$. These non-trivial phases can be seen as encoding anyon-like statistics. From this viewpoint, the Federbush model is a toy model for topological features of entanglement in one space dimension. In this paper we show that, for an infinite system, these topological features play no role when computing many known measures of entanglement at equilibrium in the ground state. This conclusion applies also to the post-quench dynamics after a small quench of the topological parameter.

The Hubble tension is usually formulated as a disagreement between two determinations of a single scalar parameter, $H_0$, within an isotropic FLRW model. We develop a quantitative framework treating the tension as a consistency test of the scalar FLRW compression of cosmological data in a homogeneous, anisotropically expanding Bianchi type I background. Beyond synthesizing established results on Bianchi I kinematics, null geodesics, and optical propagation, our original contribution is a worked weak-shear, axisymmetric calculation mapping a specified shear history into a low-redshift luminosity-distance quadrupole. The calculation explicitly separates the direction-dependent redshift–affine-parameter mapping from the Jacobi-focusing contribution, propagating the resulting distance quadrupole through an analytic polar-cap toy window. For freely decaying shear, we obtain $A_D(z) = -B_{H0} + (2q_0-1)B_{H0}z/2 + (5-q_0-18q_0^2+6j_0)B_{H0}z^2/12 + O(z^3, B_{H0}^2)$, where $B_{H0}=(H_{\parallel 0}-H_{\perp 0})/H_0$ and $j_0$ is the mean jerk parameter. A representative BBN limit, $\Omega_{\sigma 0} \le 10^{-23}$, implies $\vert{}B_{H0}\vert{} \le 9.5 \times 10^{-12}$ and a distance-modulus quadrupole below $2.4 \times 10^{-11}$ mag at $z=0.15$. The early-Universe bound used is adopted from prior work; the novelty lies in propagating it through the derived Sachs–Jacobi mapping into limits on the luminosity-distance quadrupole and catalogue-window bias. By contrast, a 1% directional shift requires $\Omega_{\sigma 0} \approx 2.5 \times 10^{-5}$, while matching the Planck 2018–SH0ES 2022 separation requires $\Omega_{\sigma 0} \approx 1.8 \times 10^{-3}$. Thus, the minimal shear-only model cannot resolve the tension, though the framework supplies a falsifiable programme for testing late-time anisotropy with SNe, BAO, and standard sirens.

We study superconformal indices in the presence of line operators in S-fold theories. We consider two types of lines, realized by fundamental strings and fivebranes, respectively, in AdS$_5 \times S^5/\mathbb{Z}_k$. For fundamental lines, we analyze the corresponding indices including finite-$N$ corrections arising from giant graviton configurations. For $k=2$, we compare the holographic results with line operator indices in $\mathcal{N}=4$ super Yang-Mills theories with orthogonal gauge groups. For $k=3,4$ and $6$, we focus on the rank $2$ case, in which the supersymmetry is enhanced to ${\cal N}=4$, and compare them with the corresponding Wilson-'t Hooft line operator indices. In both cases, we find improved agreement once giant graviton contributions are included. For line operators realized by fivebranes, after confirming agreement for $k=2$, we construct BPS configurations for $k\geq 3$ explicitly using fivebrane junctions and derive the indices in the large $N$ limit by the mode analysis on the fivebrane junctions.

In this paper, we investigate scattering of a scalar field near a Schwarzschild black hole through its $S$-matrix. Within this framework, we obtain a novel derivation of Hawking radiation by computing the emission rate, which yields a Bose–Einstein distribution with temperature $T_H=(8\pi GM)^{-1}$, the Hawking temperature. In addition to Hawking radiation, the S-matrix exhibits antibound states, corresponding to excitations at the threshold of becoming scattering (bound) states if the potential is decreased (increased). We interpret these excitations as constituents of the black-hole quantum atmosphere: a thermalised region outside of the event horizon, which is the source of the Hawking radiation. Using the spectrum of antibound states, we found the atmospheric radius, $r_{\text{Atm}} \approx 2.77 r_{s}$, which is in good agreement with previous results in the literature obtained through other methods. Our results indicate that, at the macroscopic level, the quantum atmosphere behaves like an ordinary thermalised gas at the Hawking temperature.

We study chiral symmetry breaking in the Nambu-Jona-Lasinio model on a de Sitter background, treating it as a non-renormalizable effective field theory with a physical ultraviolet cutoff. Using exponential proper-time regularization, we obtain an exact solution for the constituent fermion mass in the strong-curvature regime via the Lambert $W$ function. The consistency condition for real-valued solutions leads to an upper bound on the cosmological constant, indicating a limitation of the mean-field description rather than a fundamental physical constraint on the spacetime geometry.

We investigate the excitation region of black hole quasinormal modes (QNMs) from both analytical and numerical perspectives. On the analytical side, we propose that the QNM excitation radius is identified by the dominance switching of WKB solutions across an anti-Stokes line. Based on this picture, we derive the condition for the QNM excitation radius in Kerr spacetime. In the Schwarzschild limit with mass $M$, we reproduce the previously known value $r=2.556929 M$, which differs from the light ring radius $r=3M$. We also show that the excitation radius is independent of the angular mode $\ell$ in the high-overtone limit. As an independent approach, we employ the numerical convergence test of QNM-plus-tail expansion and obtain values consistent with the Stokes geometry in the high-overtone limit at low and intermediate spins. In the extremal limit, the QNM convergence radius approaches the outer horizon, which is captured by the Stokes geometry of the zero-damping modes, rather than the high-overtone limit. This is consistent with the fact that the ringdown is dominated by zero-damping modes in the extremal limit. Based on the complementary analysis of Stokes geometry and the convergence test, we argue that in general, the QNM excitation radius depends on the QNM overtone number, giving rise to an effective QNM convergence region.

In this study, we investigate strange quark stars (SQSs) admixed with scalar dark matter (DM), focusing on the role of microscopic interactions versus purely gravitational coupling. Our results demonstrate that while the interacting one-fluid model yields viable configurations with M_TOV > 2M_sun that satisfy current pulsar M-R measurements alongside the tidal deformability (Lambda) constraints from GW170817, the noninteracting two-fluid model more robustly meets both existing GW170817 limits and the tighter Lambda bounds anticipated from next-generation gravitational-wave detectors.

LHC measurements now reconstruct all fifteen parameters of the $t\bar t$ two-qubit spin density matrix, which amounts to a full quantum tomography of the pair. We show that this data constrains CP violation in the top-Yukawa coupling. The coupling enters the density matrix at one loop and produces spin correlations that are odd under CP and do not affect the cross section. Using the first complete renormalized one-loop density matrix and the experimental covariance, we obtain complementary constraints comparable to those from direct tree-level $t\bar t H$ and $tH$ production.