Papers

We study the confinement phase transition in SU($N_{c}$) pure Yang-Mills theory at finite $\theta \neq 0$ using the Improved Holographic QCD (IHQCD) model. We show that the critical temperature, as a function of $\theta$ for large but fixed $N_{c}$, is reduced, thus decreasing the amount of supercooling in the confinement phase transition. Upon completion of the confinement phase transition, a network of domain walls can be produced, owing to the multi-branched vacuum structure of Yang-Mills theory at finite $\theta$. We highlight the potential interplay between the produced domain walls and the confinement phase transition dynamics. We emphasize that DW production from bubble coalescence in strongly coupled non-conformal FOPTs is a dynamical process of vacuum assignment, hydrodynamics, and local reheating effects, all potentially affecting the approach towards the scaling regime. Lastly, we demonstrate the level of tuning necessary for potentially interesting imprints from gravitational waves through domain wall annihilation and its interplay with the confinement PT.

We investigate the dc magnetoconductivity of two-dimensional Dirac cones and gapped nodal rings (GNRs) subjected to a perpendicular magnetic field, which quantises the electronic spectrum into Landau levels (LLs). Working in the ultraquantum limit, where only the lowest LL (LLL) is partially occupied, we employ the Kubo–Bastin formalism to compute the transport coefficients for pointlike, Gaussian, and Yukawa impurity-potentials. For the Dirac case, the longitudinal conductivity is field-independent for pointlike impurities and a monotonic function of $B$ for the Gaussian and Yukawa potentials, while the Hall conductivity vanishes identically owing to the particle-hole symmetry of the two neighbouring LLs. The GNR case is qualitatively different: its non-monotonic stretched-checkmark LL spectrum causes the effective LLL to migrate to successively lower indices as the field increases, producing a pronounced oscillatory structure in both conductivities. The longitudinal response develops resonant peaks at LLL degeneracies, while the Hall conductivity traces out a sawtooth pattern with sharp zero-crossings at these same points. These results establish distinct transport fingerprints for the two systems in the extreme quantum limit, and provide a theoretical framework for interpreting magnetotransport experiments on GNRs.

We investigate gravitational memory beyond null infinity by studying finite-distance null hypersurfaces endowed with Carrollian geometry. We show that the intrinsic degenerate geometry, optical data, and null Brown–York tensor of a finite null screen define a quasilocal Carrollian dissipative system, providing a natural framework to characterize the residual geometric response after the passage of radiation. To make this construction explicit and compare it with the standard asymptotic description, we use Robinson–Trautman spacetimes as an exactly solvable radiative setting. For asymptotically flat Robinson–Trautman geometries, we transform the solution to Bondi gauge and extract the asymptotic data directly in terms of the Robinson–Trautman field. In the linearized sector, the Bondi shear is purely electric and produces the standard displacement-memory effect associated with the relaxation toward the final Schwarzschild geometry. We show that the leading large-radius tracefree component of the finite-screen memory reduces to the Bondi displacement memory, while finite-distance corrections retain additional focusing, embedding dependence, angular drift, Coulombic data, and near-zone information. Thus, Bondi memory emerges as the universal asymptotic projection of a broader quasilocal Carrollian response. Late-time screens approaching the final Schwarzschild horizon exhibit exponentially decaying non-isotropic Carrollian data, leaving only the isotropic null Brown–York stress. As a by-product, we construct the Robinson–Trautman solution with nonzero cosmological constant to second order in the radiative amplitude and use the holographic dictionary to study the associated energy fluxes and find that the resulting charge does not obey a universal monotonicity property.

Black-hole thermodynamics has been reproduced with remarkable success from the BFSS matrix model, but the corresponding test in the closely related IKKT matrix model has awaited its recently proposed finite-temperature formulation, within which we investigate this correspondence. Introducing a cubic Myers term, we compute the complete one-loop thermodynamics – free energy, internal energy, entropy, and heat capacity – of a fuzzy $S^2$ background, and compare against the D0 and D2 black holes as the closest available reference points, since no gravitational dual is known for this specific background. At fixed Myers coupling, the leading entropy exhibits an $O(N^3)$ scaling rather than the $O(N^2)$ behavior characteristic of conventional black holes. Holding the physical radius fixed instead yields a genuine $O(N^2)$ scaling, showing that the power of $N$ depends on the large-$N$ prescription and is therefore not by itself an unambiguous test of a black-hole interpretation. We further find no intrinsic Hawking temperature – only a characteristic scale – and a heat capacity that is negative at low temperature but positive at high temperature. The absence of an intrinsic Hawking temperature, tied to the missing gravitational dual rather than to the choice of large-$N$ prescription, persists in either scaling limit. Rather than establishing a black-hole interpretation of the finite-temperature IKKT matrix model, these results provide a quantitative benchmark against which future analytical, numerical, and holographic investigations can be tested.

We have studied the shear viscosity, bulk viscosity and associated observables of baryon asymmetric hot QCD medium subjected to weak momentum anisotropy induced by the asymptotic expansion of the medium during the early stages of ultrarelativistic heavy-ion collisions. The shear and bulk viscosities are evaluated by solving the relativistic Boltzmann transport equation within the relaxation time approximation in a kinetic theory framework. We have further analysed the Prandtl number, the Reynolds number, specific shear viscosity, and specific bulk viscosity, characterizing the sound attenuation, flow properties, fluidity, and conformal behavior, respectively. The interactions among the constituent partons are incorporated through the anisotropic quasiparticle distribution functions, with the medium characterized by finite temperature, momentum anisotropy and baryon asymmetry. Our analysis shows that both shear and bulk viscosities decrease with increasing anisotropy in both baryonless and baryon asymmetric media. In contrast, finite baryon asymmetry enhances both viscosities compared with their baryonless counterparts. The effects of expansion-induced anisotropy remain pronounced in both the baryonless and baryon asymmetric media, leading to substantial modifications of the associated viscous observables. These features are attributed primarily to the squeezing of the parton distribution functions caused by expansion-induced momentum anisotropy, together with the resulting modification of the partonic dispersion relations. Our results demonstrate that the expansion-induced anisotropy significantly influences the sound attenuation, flow characteristics, fluidity and conformal behavior of baryon asymmetric hot QCD medium, providing new insights into the viscous properties of the medium created in ultrarelativistic heavy-ion collisions.

We investigate the propagation of classical plane waves and surface plasmon-polariton modes within the framework of pseudo-electrodynamics (PED) supplemented by a non-local Chern-Simons (CS) topological term. Starting from the dimensionally reduced action, we derive the decoupled second-order wave equations for the electromagnetic field, and for the gauge-potential. In vacuum, we show that the topological CS parameter works as a dynamical mass generator, modifying the strict transversality of plane waves, and introducing a distinct energy gap in the dispersion relation. Considering a planar conducting medium that satisfies the Ohm law, the topological mass induces a novel hybridization mechanism between the Transverse Electric (TE), and Transverse Magnetic (TM) modes, a feature entirely absent in the conventional planar plasmonics. We analyze the asymptotic limits of this system, obtaining the exact real solutions in the lossless reactive Drude regime, and deriving the complex refractive index through a quasi-local approximation in the dissipative regime.

We compute the viscoelastic and thermal response of non-homogeneous hadronic condensates at finite baryon density representing crystals of baryonic tubes and layers. We describe them using analytic solutions of the Skyrme model in $3+1$ dimensions as ground states for a perturbative approach. At low enough temperatures, the lowest-energy excitations are described by a free massless scalar field theory in $1+1$ dimensions. We apply the Green-Kubo formulas to such excitations to obtain the elasticity tensor and other response coefficients. The analytic results of our computations are compared with available results on the nuclear pasta phase.

Where does the Standard Model's internal structure come from? Treating $\mathbb{O}\oplus\mathbb{H}\oplus\mathbb{C}\oplus\mathbb{R}$ as a module for its own multiplication algebra enables a particular origin story for the Standard Model's pre-Higgs, $\mathfrak{g}_{SM}:=\mathfrak{su}(3)_{C} \oplus \mathfrak{su}(2)_{L} \oplus \mathfrak{u}(1)_{Y},$ and post-Higgs, $\mathfrak{g}_{LE}:=\mathfrak{su}(3)_{C} \oplus \mathfrak{u}(1)_{Q},$ symmetries. In this model, weak hypercharge and electric charge operators, $Y$ and $Q,$ take on a remarkably simple form: $\sum \frac{1}{n}\mathbb{I}_{n\times n}$. Upon the introduction of Cayley-Dickson imaginary units, this 15 $\mathbb{R}$ dimensional $\mathbb{O}\oplus\mathbb{H}\oplus\mathbb{C}\oplus\mathbb{R}$ embeds naturally as a vector space into several well-studied 16 $\mathbb{R}$ dimensional algebras, which we generically refer to as $\mathbb{V}.$ With this embedding, the Standard Model's internal symmetries may then be seen to arise in part from the sequence of nested inclusions: $\mathbb{R}\subset\mathbb{C}\subset\mathbb{H}\subset \mathbb{O}\subset\mathbb{V}.$ In the sedenionic case of $\mathbb{V}= \mathbb{S}$, the full sequence becomes a Cayley-Dickson tower. We define the notion of endomorphic models of particle physics, and connect $End_\mathbb{R}(\mathbb{V})\simeq Cl(0,8)$ to the earlier ideas of Bott Periodic Particle Physics. We comment on a possible connection between the existence of multiple complex structures and the baryon asymmetry problem. In closing, we identify an appearance in this model of the fully connected tree of division algebraic Hopf fibrations that starts at $S^{15},$ and simultaneously involves the four parallelizable spheres $S^7, S^3, S^1, S^0.$

While the cosmological implications of the Swampland Conjectures are usually discussed in the context of inflationary model building, they also have implications for the violent, non-adiabatic dynamics that can follow inflation or any displacement of string moduli. We study this question through the lens of self-resonant preheating, where we point out that two Swampland motivated structures play central roles. The first is the local curvature of the potential: the tachyonic branch of the refined de Sitter Conjecture singles out the kind of negative curvature that can drive tachyonic amplification. We show, however, that local curvature data is not enough; the large field asymptotics of the potential determines how the modulus samples the unstable region. Thus, plateaus, barriers, and runaways can lead to different resonance efficiencies; we study tachyonic resonance for bulk moduli in LVS and KKLT compactifications, as well as for typical blow-up moduli potentials and alpha-attractor models. The second Swampland motivated structure pertains to the tower of light states predicted by the Swampland Distance Conjecture. Modeling a finite subset of such states as an effective stochastic environment within which a string modulus preheats, we find that the light states mainly reshape existing resonance bands by smearing, shifting, and mildly seeding instabilities, rather than opening a robust new reheating channel. Our results suggest that Swampland physics affects preheating by controlling both the deterministic curvature structure of the potential as well as stochastic corrections from emergent light states.

We study the partition function of five-dimensional $\mathcal{N}=1$ $U(N)$ supersymmetric Yang-Mills (SYM) theory with an adjoint hypermultiplet of mass $m_{\rm adj}$ on a toric Kähler surface $S$ times a circle of radius $\boldsymbol{\beta}$. Extending earlier work in $\mathcal{N}=2^*$ SYM theory on $S$, and in pure $\mathcal{N}=1$ SYM on $S\times \mathbb{S}^1_{\boldsymbol{\beta}}$, we find that the path integral localizes to an integral along the Cartan torus of the product of Nekrasov 5D partition functions for each affine patch. Restricting to the gauge group $U(2)$ for simplicity, the integrand has an infinite set of poles of degree at most $\chi(S)-2$. With a natural prescription for integrating around such poles, we find that the contributing poles are in one-to-one correspondence with the torus-fixed points in the moduli space of semi-stable torsion-free sheaves on $S$. Moreover, for non-even first Chern class, their contributions are independent of the equivariant parameters $\epsilon_1,\epsilon_2$ and add up to the $\chi_{y^2}$-genus of that moduli space, where $y^2=e^{-\boldsymbol{\beta} m_{\rm adj}}$, and hence coincide with the refined Vafa-Witten invariants. For even Chern class, the partition function depends on the equivariant parameters $\epsilon_1,\epsilon_2$ as well as $y$, and its relation to rational, refined Vafa-Witten invariants remains unclear.

In this paper, we study the coherence/decoherence of a quantum harmonic oscillator in anti-de Sitter (AdS) spacetime by quantising the graviton in a curved background with a nontrivial boundary condition. In the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order in G and 1/omega^2, where omega is related to the trapped frequency of the harmonic oscillator. We will proceed with a semi-Markovian analysis to compute the Lindbladian equation and estimate the decoherence rate and selection rules at the leading order, which come in two kinds: one responsible for the local interaction between matter and graviton, and the other related to the AdS global curvature. The latter determines the recoherence of the quantum system for a certain choice of the trapped harmonic oscillator's frequency and the global curvature. We also demonstrate that we recover the flat spacetime limit by taking appropriate approximations.

We propose a second-order partial differential equation method to solve multi-loop Feynman integrals as an equilibrium problem. As a proof-of-concept demonstration, we perform a Galerkin discretization of the corresponding variational form and employ the finite element method to compute two-loop four-point Feynman integrals. This method can solve the integral over a broad region of multi-dimensional phase space once and for all. This work establishes a new connection between perturbative quantum field theory and modern partial differential equation methods, with the potential to streamline a wide range of phenomenological applications.

We compute numerical warped Type IIB flux backgrounds on Calabi-Yau threefolds following the construction of Giddings, Kachru, and Polchinski. Using physics-informed neural networks, we approximate all three ingredients required by the GKP setup: the Ricci-flat Calabi-Yau metric, the harmonic (2,1)-forms representing the imaginary self-dual three-form flux, and the warp factor, which solves a sourced Poisson equation on the internal manifold. We apply our pipeline to the Dwork family of quintics for two different flux vacua, one near a conifold point and one away from it, the latter serving as a numerical cross-check. With these tools, we study the singular bulk problem, and find that for our benchmark point close to the conifold, approximately 0.5 percent of the total Calabi-Yau volume sits in the throat, and the warp factor is an order of magnitude larger as compared to the bulk. We also introduce several improvements to techniques used for numerical studies of CY metrics and quantities derived from them that might be of interest independently of our application. These include an improved point sampling algorithm that produces samples that are more uniform under the Calabi-Yau measure, a feature-engineered spectral network for the metric, multi-step physics-informed training, and a weighted Huber loss tailored to stiff PDEs with highly non-uniform sources.

Quantum gravity impacts Standard Model fields through effective interactions generated by renormalization. These appear as Standard Model Effective Field Theory (SMEFT) operators, where the effects of new physics are parametrized by the values of the higher-order SMEFT coefficients. As a step towards predicting these SMEFT coefficients from the asymptotically safe Standard Model with quantum gravity, we investigate the flow of a representative set of four-fermion operators under gravitational fluctuations. We strengthen the evidence for the near-perturbative nature of asymptotic safety by finding that these dimension-six-interactions remain irrelevant, resulting in the prediction of specific values for the dimensionless ratios of SMEFT coefficients in the IR. We also find a mechanism that can make a specific subset of these operators relevant. This subset is determined by symmetry considerations. On this basis, we provide a categorization of dimension-six-SMEFT interactions into two categories. Interactions in the first category are predicted to be non-zero, but Planck-scale suppressed. Interactions in the second category are predicted to be zero at small gravitational coupling, but may become free parameters of the theory at larger gravitational couplings.

We show that the derivative expansion of the exact (functional) renormalization group is a divergent series in any dimension, both for an exponential cutoff and more general smooth cutoffs. We prove this by showing that within massless $\lambda\varphi^4$ perturbation theory, such divergences arise first at two loops. From several lines of theoretical argument and by analysing infinite classes of two- and three-loop contributions, we conclude that the derivative expansion is an asymptotic series that initially converges towards the exact result before divergent behaviour takes over.

A variety of examples of gauge/gravity duality have a Coulomb branch for the gauge theory dynamics. We exploit this feature to construct an S-matrix, in which the initial state is a shell of branes converging on the origin of the Coulomb branch. In the gravitational dual, the shell of branes sources a geometry with a capped throat; the cap descends from the asymptotic region to larger and larger redshift. A trapped surface forms when the redshift of the cap reaches the point where the excitation of strings stretching between the branes is unsuppressed, and the dual gauge theory deconfines. The intermediate state is a long-lived black hole, which then decays via the slow emission of branes back onto the Coulomb branch. We compare and contrast the descriptions of this process in the bulk effective field theory and the dual gauge theory; and discuss the consequences of this construction for the black hole information paradox.

We investigate how localized quantum corrections to the inflaton potential affect preheating dynamics and the resulting stochastic gravitational wave (GW) spectrum. When these corrections sufficiently suppress the quadratic term of the potential near its minimum, inflaton self-resonance can produce a peaked GW spectrum. On the other hand, we find that a smooth and enhanced spectrum can appear if the quadratic term acquires a negative coefficient. As a concrete realization, we analyze the $\alpha$-attractor T-model with a one-loop Coleman–Weinberg correction induced by a heavy scalar and compute the resulting GW spectra using lattice simulations. The GW signals lie in the ultra-high-frequency regime at frequencies above the kHz range. These results suggest that GW signals from preheating may probe quantum corrections to the inflaton potential, thereby providing indirect information about the underlying UV physics.

Characters of rational conformal field theories solve modular linear differential equations labelled by their order and the Wronskian index $\ell$. Direct classification of admissible solutions by solving MLDEs becomes increasingly difficult at higher $\ell$ – where movable poles and accessory parameters appear. In this work we introduce differential operators that relate higher-$\ell$ solutions to lower-$\ell$ ones while preserving modular covariance and integrality of the \(q\)-series. In rank two, this generates all allowed Wronskian sectors from the Mathur–Mukhi–Sen equation. In rank three and higher, it reduces the construction of higher-$\ell$ quasi-characters to simpler equations with lower $\ell$. This gives an efficient new route for organising candidate RCFT characters, and more generally quasi-characters, across the Wronskian tower. As an application, we apply our construction to prove a previously conjectured property on the signs of $\ell=2$ quasi-characters in rank 2.

We construct the soft gluon light cone wave function of a fast moving hadron and the associated unitary evolution operator $\Omega$ up to $\mathcal{O}(g^{2})$ in pure Yang Mills theory $(N_{f} = 0)$, within the Color Glass Condensate (CGC) framework. Working in light cone gauge, we perform a Born Oppenheimer separation between fast valence and soft modes and implement the eikonal approximation, which allows $\Omega$ to be written as a fully normal ordered series in soft gluon creation and annihilation operators. The expansion coefficients are functionals of the non-commuting valence color charge density operators $\rho$. We fix the coefficients by using the unitarity and explicit diagrammatic calculations within light-cone perturbation theory (LCPT). As an application, we diagonalize the pure Yang Mills soft Hamiltonian through orders $g$ and $g^{2}$ and show that the off diagonal mixing elements between Fock sectors cancel leading to the coherent background field energy proportional to $\rho^{2}$.

The cosmological collider program probes ultra-high-energy physics by searching for subtle oscillatory signatures induced by inflationary particle exchange. Due to the non-linear symmetries usually assumed in inflation, these signals do not appear in isolation; moreover, their amplitudes are bounded by perturbativity and unitarity. To comprehensively probe cosmological collider physics, we must jointly analyze the full multi-field inflationary Lagrangian: in this work, we conduct such a study, probing single, double, and triple scalar field exchange and self-interactions across a wide range of masses (in both the complementary and principal series), mixings, and sound-speeds. Using modern theoretical tools (including the cosmological bootstrap and the cosmological flow), we construct a vast library of tree-level primordial bispectra: combining these with recent measurements of the inflationary shape function from Planck and modern sampling techniques, we perform Bayesian exploration of the eight-parameter multi-field likelihood. Most previous studies of cosmological collider physics assume weak mixing, such that the coupling between the scalar field and the Goldstone mode can be treated perturbatively: in our companion study, we demonstrate that this assumption is incompatible with current datasets except at the smallest masses. By solving for the inflationary bispectra numerically using CosmoFlow, we perform the first analysis of the strongly-mixed collider, demonstrating that the Planck constraints are much tighter than the theoretical bounds, though the oscillatory contributions are heavily suppressed. Across the full multi-field landscape, we find no evidence for new physics with a maximal $\chi^2$ improvement of $5.3$.

Future interferometers may detect a gravitational-wave (GW) signal from a cosmological first-order phase transition. Reconstructing the underlying particle-physics model from such a signal requires theoretical control over the map from microphysics to the spectrum. For classically scale-invariant extensions of the Standard Model, which generically predict strongly supercooled transitions and strong GW signals, this map depends sensitively on the treatment of quantum and thermal corrections to the nucleation rate. Taking the classically conformal ${\rm U}(1)_X$ model as representative of this class, we scan its parameter space and compare two resummation schemes. The first is a high-temperature effective field theory, matched at two-loop level and including next-to-leading-order corrections to the bounce action, with the nucleation-rate prefactor given by the full one-loop functional determinants. The second is a commonly employed daisy-resummed effective potential, with the prefactor estimated on dimensional grounds. Reconstructing the fundamental model parameters through a Fisher-matrix analysis of injected GW signals at LISA, we find that the daisy-resummation scheme is strongly disfavored, as its theoretical error dominates over the reconstruction uncertainty.

Massive cosmological correlators exhibit a rich hypergeometric structure already at tree level, reflecting the distorted propagation of particles in de Sitter spacetime. In this paper, we reveal that this apparent complexity conceals a remarkably simple underlying mathematical structure. Using the spectral representation, we compute arbitrary tree-level correlators of scalar fields with generic masses and show that they are constructed from fundamental building blocks belonging to the family of Lauricella generalised hypergeometric functions, glued together by spectral integrals. We develop a spectral gluing algorithm that evaluates these integrals through elementary graph combinatorics, yielding explicit series representations that resum the dependence on internal energies away from soft limits. This algorithm naturally generates solutions to the differential equations satisfied by massive correlators as expansions in the corresponding eigenfunctions. Acting with a set of graph annihilators, we uncover a new class of magical identities among generalised hypergeometric functions, revealing an unexpected simplification: once the dynamical propagators are stripped away, the remaining hypergeometric kinematic dependence collapses to rational functions. Our results expose a hidden simplicity in the rigid hypergeometric analytic structure dictated by graph combinatorics, and hint at an intrinsic geometric principle from which properties of massive correlators naturally emerge.

A compact form of the stress tensor $\langle T^{ab}T^{cd}\rangle$ correlation function of a quantum scalar field of arbitrary mass $m$ and curvature coupling $\xi$ is presented, with particular emphasis on decoupling in the $m\to\infty$ limit and infrared origin of the conformal anomaly as $m \to 0$. The Ward Identity (WI) of covariant conservation is verified for the full second order metric variation of the one-loop effective action, of which $\langle T^{ab}T^{cd}\rangle$ is part, including local contact terms. This WI is satisfied by two tensors, one spin-2 (traceless) and the second spin-0 (traceful), each multiplied by a Lorentz invariant form factor computed in $n$-dimensional regularization. Minimal subtraction of pole terms at $n =4$ produces form factors that fail to satisfy decoupling for general $\xi \neq 1/6$, but can be simply amended to do so. Particular interest attaches to the $\xi=1/6$ case, in which the spin-0 form factor at $n =4$ is completely finite, requires no UV regularization or subtractions, and satisfies decoupling directly. Its imaginary part defines a spectral function that obeys a UV finite sum rule for any $m$, while its real part unambiguously determines the $\square R$ in the massless limit. Its $m^2$ dependence describes a Wilsonian renormalization group flow to an effective field theory limit at large distances. At $m= 0$ the spin-0 spectral function becomes a Dirac $\delta$-function at zero energy, demonstrating the existence of a massless scalar Goldstone collective excitation due to the conformal anomaly in the low energy effective theory of gravity.

We study scalar theories obtained by pulling a free massive multiplet back through a polynomial field redefinition with constant unit Jacobian. Our main example uses the three-variable noninjective map recently announced by Alpöge. After a linear normalization, it defines a three-scalar sigma model with a flat, unit-volume field-space metric and three isolated vacua. Each vacuum is locally described by three free modes of mass m, and the exact equations of motion reduce locally on each sheet to free Klein–Gordon equations. The global theory is nevertheless not a single free theory: the field-space metric is incomplete, the number of real preimages changes across target space, and the commuting position operators have nonconstant joint spectral multiplicity. This rules out a global unitary implementation of the field redefinition and a regular Weyl exponentiation of the formal canonical momenta. We then analyze a four-scalar map with a generic quintic fiber. It exhibits the same mechanism with an additional field that controls the fiber polynomial. The two examples separate perturbative equivalence on a chosen local sheet from global quantum equivalence of the full field space.

Following approach of Iorgov–Lisovyy–Teschner, we construct solutions of the (modified) Riemann–Hilbert problem using conformal blocks of $(1,k)$ Virasoro models. For $k>1$ case, the solution of this Riemann–Hilbert problem is not unique due to more singular behavior at punctures. On the CFT side the dimension of the space of conformal blocks also increases. We specifically study the $k=2$ case, which corresponds to the central charge $c=-2$ and symplectic fermions. We explicitly construct a corresponding solution of the modified Riemann–Hilbert problem in the case of 3 punctures and prove its uniqueness under suitable initial data conditions. We also obtain new bilinear relations for $c=-2$ tau functions.

We revisit the holographic proposal relating the growth rate of spread complexity to the radial momentum of a bulk probe, aiming to identify its underlying assumptions and clarify how classical probe dynamics emerges from quantum dynamics. By quantizing AdS probes directly and using the extrapolation dictionary, we provide a more general derivation of the proposal. In particular, we interpret it as a concrete realization of a classical complexity observable and its quantization in the “complexity=anything” framework. Since probe dynamics is not intrinsically tied to the AdS/CFT correspondence, we also examine the proposal in flat and de Sitter spacetimes. In flat spacetime, the physical Hamiltonian does not preserve the coherent-state structure, and spread complexity measures the dispersive broadening of the wave packet rather than classical momentum. In de Sitter space, generic semiclassical wave packets in the static-patch energy representation show the same dispersive behavior. By contrast, coherent states adapted to the principal-series representation can exhibit exponential growth of spread complexity, with a growth rate that has the same time dependence as the classical radial momentum. These examples indicate that a semiclassical limit alone is not sufficient for a momentum–complexity relation.

We develop a framework for minimally perturbing local measurements in relativistic quantum field theory, with the aim to sense local properties of the field in a non-destructive manner. The field properties are sensed by weakly coupled pointers and encapsulated in conditional expectation values dependent on a postselection of the field state. Our operational protocol uses causally admissible Kraus updates for the field, in line with recent relativistic measurement theories, keeping in mind restrictions related to “impossible measurements”. We illustrate our approach with three applications: a spacelikeness detector for causal-structure sensing, counting particle-creation densities in a supercritical potential and non-destructive discrimination between entangled states of the field and mixtures.

Timelike entanglement entropy (tEE) has recently emerged as a novel probe of temporal quantum correlations in gravitational systems. Existing studies are largely restricted to static backgrounds. In this work we extend the construction of tEE to an evaporating Schwarzschild–AdS black hole. The evaporation is modeled through an effective Stefan–Boltzmann description of Hawking radiation coupled to an external absorptive bath, yielding a time-dependent horizon radius ($r_h(t)$) and surface gravity $\kappa(t)$. We derive, from the near-horizon Rindler structure of the evolving horizon, an adiabatic generalization of the static Kruskal construction, obtaining the accumulated thermal phase $\Phi(t)=\int_0^t\kappa(t')\,dt'$ as the natural replacement for the static phase $\kappa t$. The validity of this construction is governed by an explicit adiabatic parameter $\mathcal A(t)$, which we verify numerically remains small ($\lesssim0.012$) throughout the regime of interest. It vanishes exactly where the horizon crosses the critical radius $r_h=l/\sqrt3$ identified independently from the static thermodynamics. Using $\Phi(t)$, we construct a dynamical timelike entanglement entropy that continuously tracks the evaporation process and derive the corresponding dynamical Page-like times. Unlike the uniformly spaced Page-like times of the static geometry, evaporation induces non-uniform temporal spacing, together with a progressive phase delay and amplitude modulation of the oscillatory tEE. Because the dynamical entropy depends on the full accumulated history of $\kappa(t)$ rather than its instantaneous value alone, it retains a memory of the entire evaporation process. These results establish a first-principles dynamical framework for investigating temporal quantum correlations in evaporating black holes.

For an arbitrary renormalizable ${\cal N}=1$ supersymmetric theory with a single gauge coupling regularized by higher covariant derivatives we calculate the three-loop contribution to the anomalous dimension of the matter superfields proportional to the sixth powers of Yukawa couplings for a wide class of renormalization prescriptions. Next, taking into account that in the case of using the higher covariant derivatives supplemented by minimal subtractions of logarithms the NSVZ relation is valid in all orders, we calculate the corresponding four-loop contribution to the gauge $\beta$-function and investigate its scheme dependence. In particular, we construct the so-called “minimal” renormalization prescription for which the renormalization group functions have the simplest possible form provided that the exact equations for the gauge and Yukawa $\beta$-functions following from supersymmetry remain valid.

We analyze the ultraviolet divergence structure of meson susceptibilities in finite-temperature QCD, for lattice formulations with exact chiral symmetry. The bare susceptibility separates into additive divergences and a multiplicative renormalization $Z_\Gamma^{2}$. The additive divergences are temperature-independent, and are removed by the temperature subtraction. They consist of the leading power divergence $\alpha_\Gamma/(2a^2)$ from the identity operator, together with a mass-dependent logarithmic term $\propto m^2\ln(1/(am))$. Exact chiral symmetry forbids all mass-dependent power divergences of the susceptibility. The multiplicative factor $Z_\Gamma^{2}$ has a logarithmic dependence on the lattice spacing, controlled by the operator anomalous dimension. We show that the symmetry ratio $\kappa_{AB} = (\chi_A^{\rm reg} - \chi_B^{\rm reg})/ (\chi_A^{\rm reg} + \chi_B^{\rm reg})$, built from temperature-subtracted susceptibilities of symmetry partners, is exactly renormalization-group invariant and scheme-independent. The additive divergence is removed by the subtraction, and the multiplicative factor cancels through the equality $Z_A = Z_B$. This equality holds for any number of flavors and any quark masses in a mass-independent scheme, unaffected by spontaneous symmetry breaking or the $U(1)_A$ anomaly. We derive the complete $Z$-factor chains for all meson channels and contrast the divergence structure with that of Wilson fermions, for which the explicit chiral-symmetry breaking induces a chiral-odd power-divergent mixing and spoils the equality $Z_A = Z_B$ on which the construction relies.