Papers

We introduce a procedure to obtain lump solutions via the formation of a kink-antikink pair, consisting of the superposition of kinks whose distance from the origin is controlled by a single parameter $a$. For large values of $a$, a wide plateau appears in the solution, which we call a large lump. The procedure involves the use of a first-order equation that allows the construction of the potential associated with the lump solution. We then investigate several known scalar field models where the parent kinks are capable of giving rise to novel lumps. The lump inherits the tails of the parent kink, allowing for either short-range exponential profiles or long-range profiles characterized by distinct power-law decays. We also show how to verify if an arbitrary lump solution can be obtained via our method and illustrate this possibility with a novel vacuumless lump.

A projective measurement of a many-body state produces a microscopic snapshot, usually viewed as random classical data. We show that partial occupation snapshots of the critical XX chain contain a universal angle with a precise conformal meaning. Dividing the ring into two measured and two unmeasured arcs, we assign geometry-dependent conformal side weights to the observed occupations and obtain a compact variable $\delta_L$. At every finite size, $\delta_L$ is fixed by the measured sites alone; the particular complete-configuration lift $X_L$ used in the proof additionally depends on unobserved particles. This angle is an exact microscopic compact coordinate whose scaling-limit law is that of the relative Dirichlet phase of the associated conformal quadrilateral—the boundary coordinate conjugate to charge in continuum post-measurement descriptions. Exact free-fermion determinants yield all of its Fourier moments. We prove that the lift becomes Gaussian with variance $2h(\zeta)$, where $h(\zeta)$ is the rectangle modulus, and hence $\langle e^{\ii q\delta_L}\rangle\to e^{-h(\zeta)q^2}$. Thus raw quantum snapshots realize the heat kernel on a circle and provide an outcome-level microscopic foundation for the compact zero-mode sector of Born averages over fluctuating conformal boundary conditions.

We show that geometric phases accumulated during adiabatic evolution can be converted into observable interference in Krylov space, leading to a geometric-phase-dependent Krylov oscillation. Adiabatic dynamics force Krylov complexity to vanish if the initial Krylov basis is an instantaneous eigenstate of the Hamiltonian; Nevertheless, we demonstrate that the Krylov complexity will be non-vanishing if the initial Krylov basis is a superposition state rather than an eigenstate. Consequently, Krylov complexity is found to depend on the difference of dynamical phases in the Krylov space, which is deeply related to the Berry connections in the original Hilbert space. In particular, for a single qubit system with constant Lanczos coefficients, Krylov complexity oscillates harmonically at a frequency given by the strength of the external field and the geometric Berry phase. Therefore, our work may provide a novel avenue to probe the geometric phase from the Krylov complexity.

We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

We consider the classical scattering of two gravitating compact objects in the presence of a massive scalar mediator, providing a simple model of exotic phenomena. Through dimensional analysis, we argue that such a process can only be classical in the presence of gravity, a consequence of which is that perturbing in the coupling of the scalar to a worldline is not separate from the post-Minkowskian expansion. When computing asymptotic observables, the massive mediator complicates the Fourier transforms to impact-parameter space at next-to-leading order. We reduce these to univariate parametric integrals - amenable to numerical integration - and produce analytic results for the linear impulse and the scattering angle to the second post-Minkowskian order. The scattering angle exhibits a maximum when the range of the scalar-mediated force is comparable to the impact parameter, a possible signature of a massive scalar mediator. In the opposite, large-mass regime we uncover a screening effect: integrating out the scalar sourced by each compact object reduces its gravitational mass by an amount linear in the scalar's mass. Both of these phenomena are next-to-leading-order effects.

Fermionic field types in arbitrary signature are often inferred from complex Spin representations alone, which obscures distinctions associated with real structures, disconnected spacetime reflections, and action-level bilinear constraints. We give a convention-explicit classification that treats the full real Clifford algebra and its even subalgebra separately, thereby distinguishing pinors from spinors and Pin-equivariant Majorana-type structures from structures that are only Spin-equivariant. Adjoint, complex-conjugation, and transposition intertwiners are combined with elementary and collective reflection lifts into a unified sign calculus. The resulting local Clifford classification is organised into thirty-two periodicity sectors determined by the Bott class and the total dimension modulo eight, without including theory-dependent gauge, anomaly, or global constraints. For each sector, we identify the available Dirac, Weyl, Majorana, symplectic Majorana, Majorana-Weyl, and symplectic Majorana-Weyl fields. The existence of an invariant pairing is distinguished from intertwiner compatibility, Grassmann and chiral selection rules, covariant index contraction, and Hermiticity of local bilinear operators.

Motivated by recent numerical studies where various $SU(2)$ Chern-Simons-matter theories emerge, we analytically study topological phases and quantum criticality in two-dimensional systems described by such theories. First, we classify $SU(2)_k$ topological orders in all lattice spin systems with a $p4\times SO(3)$ symmetry, where $k$ is an arbitrary nonzero integer. We find that for each odd $k$, the topological order can emerge in systems with an arbitrary Lieb-Schultz-Mattis (LSM) anomaly, and the symmetry cannot permute anyons. If the system has a nontrivial (respectively, trivial) LSM anomaly, then there is exactly one (respectively, nine) symmetry-enriched topological (SET) phases. On the other hand, $SU(2)_k$ topological order with any even $k$ can only emerge in systems with a trivial LSM anomaly. If $k\notin\{6, 10, 14, \cdots\}$, the symmetry cannot permute anyons, and there are 16 SET phases. If $k\in\{6, 10, 14, \cdots\}$, there are 4 different ways how the symmetry can permute anyons, and there are 64 SET phases. Next, we analyze the $SU(2)_k$ Chern-Simons theories coupled to $N_f$ flavors of gapless matter fields that can be either bosonic or fermionic. For both types of theories, we consider a joint large-$N_f$ and large-$k$ limit with $N_f/k$ fixed, and compute the scaling dimensions of the bilinear operators of the bosons or fermions to the order of $1/N_f$. These results sharpen our understanding of these emergent exotic topological phases and quantum criticality, and provide useful guidance to explore them further.

We develop the kinematical and operator-algebraic foundations of a groupoid-based relational quantum field theory (RQFT) on curved spacetimes. Indeed, the usual group-based quantum reference frame (QRF) formalism is not directly suited to generic curved Lorentzian backgrounds as global symmetry groups are typically absent or too small. We formulate a notion of QRF for a continuous groupoid. This yields a groupoid relativization map and relational observables. We show that a localization limit recovers the ordinary non-relational description. We construct canonical sharp groupoid QRFs, which form the groupoidal counterpart of the ideal group QRFs based on $L^2(G)$. We further prove that the groupoid QRF construction reduces to the standard operational QRF formalism for locally compact groups. The action groupoid QRFs are torsor QRFs only for specific classes of fields of positive operator-valued measures (POVMs), and the torsor relativization map only applies to constant operator fields of system observables. We review the foundations of RQFT in Minkowski spacetime. We prove new results that further link RQFT to Wightman QFT. We show that covariant POVMs are $\mu$-continuous with respect to quasi-invariant $\sigma$-finite positive Borel measures $\mu$. Thus, relational quantum fields can be understood as the smearing of pointwise-defined kernels with respect to the QRF's statistics. We develop RQFT in curved spacetime, where we argue that the correct replacement for the Poincaré group is the Poincaré groupoid of the spacetime. We also indicate how the framework extends further to internal gauge symmetry and relational gauge-covariant quantum field theory via Atiyah groupoids, providing a first step towards formulating a relational quantum Yang-Mills field theory.

Hawking radiation may be regarded as originating at the event horizon; however, its spatial origin can instead be distributed over a finite region outside the horizon. In this paper, using an effective proper temperature, we investigate the quantum atmosphere within a tractable model based on the two-dimensional radial sector of $D$-dimensional Schwarzschild black holes. In the Hartle–Hawking state, the proper temperature is derived from the first law of thermodynamics in the presence of the conformal anomaly associated with Hawking radiation. In the Unruh state, we decompose the proper temperature into two chiral temperatures, $T_{\rm L}$ and $T_{\rm R}$, associated with the ingoing and outgoing fluxes, respectively. Demonstrating $T_{\rm R}$ as the effective proper temperature characterizing the outgoing Hawking flux with the proper temperature in the Hartle-Hawking state, we define the atmospheric radius effectively as the radial position at which the effective proper temperature attains its maximum. We then numerically compute the atmospheric radius of the quantum atmosphere for various spacetime dimensions and show that it decreases monotonically as the number of spacetime dimensions increases. In the large-dimensional limit, we find that the atmospheric radius remains separated from the horizon by a finite radial factor, indicating that the quantum atmosphere can persist as an extended exterior region in any dimension.

We provide an unfolded formulation of linearised 6D exotic supergravity with manifest superconformal symmetry including conformal duality transformations. The construction is based on a superoscillator realisation of the metaplectic supergroup $MOSp(16|16)$ containing the Howe dual pair $MOSp(8^\ast|8)\times SU(2)$. Exotic graviton potentials arise in conformally dual pairs of two-forms in direct products of $SU(2)$-triplets and supertraceless graded-symmetric rank-two supertensors of $OSp(8^\ast|8)$ generated from a hypercharge by the supercharges, providing an analogue of the adjoint representation of $\mathfrak{psu}(2,2|4)$. The potentials are sourced via relative Chevalley-Eilenberg cocycles by a conformally dual pair of chiral and anti-chiral Weyl zero-forms valued in $SO(1,1)\times Spin(1,5)\times USp(8)$-covariant monomorphic restrictions of an extended supersingleton, i.e., an infinite-dimensional $SU(2)$-invariant Hermitian left-module of $MOSp(8^\ast|8)$ containing various irreps associated with different boundary conditions, including the unitarizable exotic supergravity multiplet. Two natural quadratic observables are i) an on-shell closed zero-form built from the chiral Weyl zero-form and its dual, akin to the on-shell value of the second Chern class on the internal twistor $Z$-space of 4D Vasiliev systems; and ii) an off-shell topological six-form built from the conformally dual pair of two-form potentials, reducing on-shell to a generating function for chiral two-point functions in super-Poincaré backgrounds.

The study of large-$N$ cases of the $O(N)$-symmetric model at criticality has attracted significant attention in recent years. In particular, a recent high-precision Monte Carlo study ( Physical Review B 105, 054428 (2022)) reported the most accurate estimates to date for the critical exponents $\nu$, $\eta$, and $\omega$ for $N \ge4$. Within the framework of the renormalization group (RG)—the cornerstone of the modern theory of critical phenomena—powerful computational approaches such as the $\varepsilon$-expansion and non-perturbative RG are available. Since the effective expansion parameter in the $\varepsilon$-expansion, $\sigma = \frac{3}{N+8}$, decreases with increasing N, one expects resummation techniques to become progressively more accurate in the large-N regime. To test this expectation, we apply the entire-hypergeometric resummation algorithm developed by Shalaby et al. to the recently obtained seven-loop divergent $\varepsilon$-series for $N \ge 4$, yielding high-precision estimates for $\nu$, $\eta$, and $\omega$ . Our analysis confirms the anticipated improvement in accuracy with increasing N. To assess the significance of these results, we note that at the same seven-loop order the $O(2)$ case exhibits errors that are an order of magnitude larger than those obtained from experiment, Monte Carlo simulations, and conformal-field-theory analysis. In contrast, for sufficiently large N, the errors in the present work are of the same order of magnitude as those from Monte Carlo and non-perturbative RG methods, demonstrating the strong predictive power of our resummation approach in the large-N regime.

We investigate holographic superconductors using modern optimisation techniques inspired by machine learning. The critical temperature is obtained by minimising the variational functional for the eigenvalue $\lambda^2$ with two complementary trial functions: a simple cosine ansatz $F(z)=\cos(a z)$ and a flexible exponential polynomial $F(z)=\exp(\sum_{n=2}^{N} a_n z^n)$, both of which automatically satisfy the standard boundary conditions. For the cosine ansatz, we perform a one-parameter minimisation and obtain $\lambda^2(\Delta)$ and $T_c/\sqrt{\rho}$ over a wide range of $\Delta$, including the exact values at $\Delta=1$ and $\Delta=2$ to high accuracy. The exponential polynomial ansatz, with up to 19 coefficients, is optimised using a multi-start L-BFGS-B algorithm with warm-starting, yielding even better agreement with known exact results. Our numerical data for $\lambda^2(\Delta)$ and $T_c/\sqrt{\rho}$ match the analytical predictions from the literature, confirming the robustness of the variational approach. This work; therefore, demonstrates that a combination of analytic trial functions and modern numerical optimisation provides a powerful, flexible, and efficient tool for exploring holographic superconductors, and can be readily extended to include backreaction or other sectors in this field.

Hamiltonian truncation offers a nonperturbative route to quantum field theory, yet its accuracy is limited by the rapid expansion of the truncated Hilbert space, which drives up computational cost. We tackle this bottleneck with a hybrid strategy that pairs classical and quantum algorithms: 1) we develop an efficient basis-generation scheme built on integer partitions; 2) we speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms; and 3) we explore quantum Krylov diagonalization as a route to the low-lying spectrum. Benchmarking against the free massive scalar and $\phi^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations.

Open system probes can provide an efficient means to characterize quantum many-body systems by employing them as engineered environments. The key idea is to map long-range spatial correlations of the environment onto dynamical correlations in the evolution of a simple quantum probe. Using the example of a qubit coupled to a transverse-field Ising model, we show how the non-Markovian rate or spectral flow can be used to identify stable and unstable fixed points, infer scaling dimensions of relevant fields, and deduce the renormalization group flow induced by deformations around any fixed point.

We examine the proposal and analysis of arXiv:2404.14477 for putting momentum waves on mazes of intersecting M2 and M5 branes by computing a family of simple examples of momentum waves on pure M5 branes. We re-analyze the BPS equations for the near-brane M5-P system with the prescribed supersymmetry structure of the full M2-M5-P system and show that the general linear system obtained in arXiv:2404.14477 captures all of the null momentum waves on the simpler M5-P system. Despite the absence of explicit M2 branes in our examples, we find that the momentum waves still localize on an AdS$_3$ factor of the AdS$_7$ associated with M5 branes, showing that the supersymmetry prescription still reflects the M2-M5-P structure. This momentum localization takes two forms: explicit singular sources and smooth, localized bump functions reflecting ”momentum migration” that is a feature of other microstate geometries. The simple, physical form of the momentum localization in our examples supports the broader proposal in arXiv:2404.14477 that independent momentum waves can localize at each brane intersection. We suggest further generalizations of momentum waves at brane intersections that could have important implications in holography.

We consider a scenario in which a black hole is enclosed in a reflecting timelike cavity and linearly perturbed. For the resulting quasinormal spectra of gravitational, electromagnetic, and other perturbations, in conjunction with our arXiv:2606.11297, we establish a thermal product formula and derive a universal asymptotic expression for high quasinormal overtones. Both results hold in asymptotically flat, de Sitter, and Anti-de Sitter spacetimes (known previously). This spectral signature directly encodes information about the black hole interior and its singularity, and is, at least in principle, accessible to an observer outside the event horizon. We then propose a concrete observational setup in which accreting plasma plays the role of a partially transmissive mirror. For small, hypothetical, primordial black holes, we argue that one may thereby be able to extract concrete information about the black hole interior from electromagnetic waves in the radiowave spectrum.

Two distinct Einstein–Hilbert sectors are related by a covariant correspondence bridge that maps stress-energy through bitensor kernels. The Bianchi identities enforce conservation, with bridge stresses balancing cross-sector exchange. For positive gravitational couplings and paired Minkowski backgrounds, a fixed metric-independent bridge leaves the quadratic action block diagonal, so the vacuum contains two massless spin-2 fields and no Fierz–Pauli mass term. A reciprocal first–order transport law generates a flux–preserving rotation of the canonical outgoing data. This divides the emitted power between visible and hidden channels while preserving the total quadrupole luminosity and the general-relativistic chirp phase. The reduced visible amplitude produces a systematic standard-siren distance shift, whose present sensitivity can be estimated from gravitational–wave catalog cosmology combined with an independent distance calibration. A source–level rescaling is physically inequivalent: it changes radiation reaction and requires compensating bridge energy flow. The construction therefore describes amplitude transfer between massless tensor channels, distinct from massive-graviton dispersion and propagation-induced oscillations.

In holography, four-dimensional confining gauge theories are often modelled by five-dimensional Einstein–scalar gravity by choosing a specific form of the scalar potential. In a large class of non-conformal theories, we show that a predictive structure emerges for the thermal confinement transition by generalising the gravitational dual to $D+1$ dimensions and using a $1/D$ expansion. These results are independent of the details of the scalar potential, hinting towards universality. The black brane geometry dual to the deconfined phase can be analytically constructed due to its effects being localised near the horizon at leading order. The solution does not exist below a minimal temperature $T_{\rm min}$ and the maximum possible supercooling in the transition $\epsilon_{\rm sc} = 1-T_{\rm min}/T_{\rm c}$ is generically suppressed by a factor of $1/D^2$. Remarkably, the maximum supercooling at the leading order is set by the speed of sound in the deconfined phase of the gauge theory at the critical temperature, $\epsilon_{\rm sc}=c_s^2(T_{\rm c})/2$. These predictions agree with explicit calculations in an exponential superpotential, improved holography, and the thermal transition in $\mathcal{N}=4$ super Yang–Mills on a sphere.

Quasi-hydrodynamics describes systems with quasi-conserved degrees of freedom, namely observables that relax on timescales that are finite but parametrically longer than microscopic relaxation times. Examples include kinetic chemistry and linear viscoelasticity. Here, we develop a rigorous effective-field-theory framework for linear quasi-hydrodynamics from kinetic-type theories. Starting from any linearized, causal kinetic-like theory endowed with slow degrees of freedom, we show that the exact dynamics of conserved and quasi-conserved observables admits a systematic expansion in the fast relaxation timescale. At zeroth order, the resulting equations form a causal, symmetric-hyperbolic theory belonging to the appropriate transient-hydrodynamic universality class, establishing Israel-Stewart-like dynamics as the universal description of slow relaxation modes. Higher-order corrections can be computed systematically and inherit universal symmetry, Onsager, positivity, and causality constraints from the underlying microscopic theory.

We study transverse vector perturbations in ghost-free extended quasidilaton massive gravity without a quasidilaton kinetic term, in the presence of minimal matter. In vacuum, we recover the known result that the kinetic coefficient $K_V$ of the gravitational vector modes vanishes on the self-accelerating branch $J=0$, so those modes are infinitely strongly coupled at linear order. We then add a canonical scalar field and a single Abelian vector (Maxwell or Proca). After integrating out the auxiliary shift, we find the same $K_V$ as in vacuum. The scalar matter has no transverse perturbation; it enters the unsimplified shift constraint, but those terms cancel once the Friedmann equation is used. A Maxwell or Proca field with vanishing isotropic background does not mix with the gravitational vectors at quadratic order. Minimal matter therefore leaves $K_V=0$ on Branch II. We do not claim that the modes are absent from the nonlinear theory. We do conclude that ordinary minimal matter is not enough to make the vector sector perturbatively healthy on this branch. If we need healthy gravitational vector modes at the linear level, Branch I is the branch to use.

We investigate the quadratic-order effective energy–momentum tensor (2EMT) of scalar cosmological perturbations on uniform-density hypersurfaces during slow-roll inflation. The 2EMT is constructed from terms quadratic in the linear metric and inflaton perturbations, and is therefore a gauge-fixed effective source rather than a gauge-invariant observable. We impose the complete scalar gauge conditions $\delta\rho=0$ and $E=0$, express all perturbations in terms of the Bardeen potential $\Psi$, and evaluate the Fourier-space 2EMT in the long- and short-wavelength domains. We distinguish the “strict” infrared and ultraviolet limits from the “intermediate” regimes. The uniform-density and comoving results agree in the strict infrared limit. In the intermediate infrared regime, the dominant leading order remains the same, while explicit finite-gradient corrections distinguish the two gauges. In the ultraviolet, the 2EMT is enhanced by $1/\epsilon$ due to the slowly varying matter clock, $\rho_0'\propto\epsilon$, and the leading uniform-density 2EMT terms exhibit an additional enhancement by $1/\sigma_2^2$ $(\sigma_2\equiv \cal{H}/k)$ from the Laplacian term. The intermediate ultraviolet expansion makes the subleading gradient hierarchy explicit without changing the leading terms. We compare these results with newly recalculated longitudinal, spatially-flat, and comoving expressions, displayed in a more explicit form than in the earlier analysis. The comparison shows that the gauge dependence is structured: uniform-density and comoving slicings coincide for adiabatic super-Hubble modes, whereas the longitudinal and spatially-flat gauges are slow-roll suppressed in the strict infrared and become gradient dominated in the intermediate infrared.

Motivated by recent DESI results suggesting dynamical dark energy, we investigate the thawing scenario in quintessence with an exponential potential, $V=V_0e^{-\lambda\phi/m_{\mathrm{pl}}}$, by analytically expanding the deviation of the equation of state parameter $w_{\phi}$ from $-1$ in powers of $\lambda$. In addition to the previously known leading-order result at $O(\lambda^2)$, we derive the $O(\lambda^4)$ correction as a function of the density parameter $\Omega_\phi$. We show that a consistent determination of the redshift dependence of $w_\phi$ through $O(\lambda^4)$ requires corrections to the background expansion. We obtain the required correction by expanding $\Omega_\phi$ in powers of $\lambda$ around its $\Lambda\mathrm{CDM}$ value. Comparison with numerical solutions demonstrates that the $O(\lambda^4)$ expansion provides a more accurate approximation than the leading-order result. Our analytical approximation, which consistently incorporates the $O(\lambda^4)$ correction, will provide a potentially useful tool for distinguishing the exponential quintessence model from other dark energy models in future observations.

Dyson universality typically manifests itself in local eigenvalue statistics. Here we show that its signature survives a nonlinear inverse-spectral reconstruction and reappears in the matrix geometry of the reconstructed operator. Using a dressing transformation, we map each unfolded spectrum to a deformation $f(x)$ of a fixed harmonic oscillator and represent it in the common oscillator basis by $F_{mn}=\bra m|f|n\ket$. We resolve the matrix-element weight into shells of fixed distance $d=|m-n|$, corresponding to the energy-transfer channels of the reference oscillator, and characterize the resulting distribution by distance-shell moments. Independently calibrated on Gaussian $\beta$-ensembles, these moments vary smoothly with $\beta$ and distinguish the GOE, GUE, and GSE. With this calibration fixed, applying the same diagnostic to the nontrivial zeros of the Riemann zeta function places the reconstructed operators in the GUE sector. Thus, the GUE character of the zeros is recovered not through direct statistics of the input levels, but from the distance-resolved geometry of the reconstructed operator.

We identify a general mechanism for the finite-time thermalization of macroscopic observables, such as coarse-grained charge densities, in terms of elementary forms of the quantum dynamics of initial states: (1) aperiodicity, which provides a computable measure of (2) a dynamical partially ergodic exploration of the Hilbert space. Specifically, this mechanism predicts the equilibration of all (concentrated) macroscopic observables, in almost all states in an initial ensemble and almost all times within finite and longer intervals, given only the observable-independent information that the return probability of the ensemble of initial states is small over a finite time range. As a special case, it also accesses standard results on equilibration over infinitely long times in terms of (stronger versions of) the effective dimension of initial state delocalization in the energy eigenbasis. Our results incorporate macroscopic thermalization into the domain of operational quantum statistical mechanics, recently developed to provide finitely computable criteria for microscopic thermalization. We discuss an overall characterization of this approach as establishing connections between (1) the decay of a (theoretically or experimentally) computable probe indicating memorylessness, (2) a fundamental invariant mechanism in terms of the alignment of observables or states in the Hilbert space, and (3) predicting different natural forms of (classical and) quantum thermalization, most of which rigorously recover conventional eigenstate-based descriptions of infinite-time thermalization as a special case but provide stronger accessible predictions over finite observation times in the thermodynamic limit.

We investigate the relation between spectral localization and entanglement harvesting in an analytically solvable model of two qubits coupled to a leaky single-mode cavity, which in turn couples to a continuous electromagnetic bath. We derive the no-jump concurrence at a prescribed reference gate time in closed form, $\mathcal C_g(Q)=2e^{-\pi/(2Q)}(1+e^{-\pi/(2Q)})/(1+3e^{-\pi/Q})$, where $Q\equiv|\Delta|/\kappa$ is the ratio of the qubit-cavity detuning $\Delta$ to the cavity linewidth $\kappa$. This reference time is inherited from the first maximally entangling unitary gate. At finite loss, $\mathcal C_g$ is the conditional concurrence at this prescribed readout time. In the high-$Q$ limit, $\mathcal C_g\simeq1-\pi^2/(16Q^2)$, while in the low-$Q$ limit it decays exponentially. For the Lorentzian spectral family, $Q$ is proportional to a detuning-normalized inverse participation ratio and simultaneously measures the balance between coherent exchange and collective decay. This yields a compact, model-specific description of the crossover from nearly unit conditional entanglement to overdamped suppression. The predicted $\mathcal C_g(Q)$ curve can, in principle, be examined in circuit QED with ideal monitoring and no-jump post-selection.

Recently we started building a bridge between two cases of Langlands duality. The latter is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic of invariant differential operators. That is strange since both items are deeply rooted in Harish-Chandra's representation theory of semisimple Lie groups. We started with the case of the group ~$SL(2n)$. In the present paper we deal with the group $SL(2n+1)$. The two mentioned groups are similar, but their representation theories is rather different.

We investigate the thermodynamic behaviour of an AdS black hole arising from nonlinear electrodynamics-corrected gravity, incorporating quantum effects through thermal fluctuations. From the Einstein–Euler–Heisenberg framework, we consider the modified black hole solution and analyse its thermodynamic properties in the extended phase space. Logarithmic and inverse-area corrections to the entropy are obtained, leading to modified expressions for enthalpy, internal energy, Helmholtz free energy and Gibbs free energy. The corrected specific heat exhibits multiple divergences and sign changes, signalling genuine second-order phase transitions and revealing a quantum-stabilized microscopic phase followed by universal macroscopic instability. Our results demonstrate that thermal fluctuations qualitatively restructure the thermodynamic phase space and highlight the dominant role of quantum corrections in governing the black hole stability.

String-derived higher-curvature scalar–tensor gravities encode microscopic coupling data in boundary response, raising the question of whether holographic observables can reconstruct the underlying higher-dimensional parameters. We answer this question for the five-dimensional string-derived Lovelock–Horndeski (SDLH) theory on its exact linear-dilaton asymptotically locally AdS branch, constructing the renormalized generating functional for an arbitrary boundary metric and spacetime-dependent scalar source. A boundary-covariant radial hierarchy unifies the variational problem, local backreaction, logarithmic obstruction, finite one-point functions, and Ward identities. Two response determinants organize the recursion, resonant obstructions, and metric–scalar mixing. The Weyl anomaly condenses into an Euler density, a Weyl-squared density, and a single curvature–scalar square whose paired variations generate the metric and scalar obstructions. The resulting renormalized functional carries string-selected coupling data into boundary geometry, operator response, anomaly coefficients, and a calculable interface with gravitational observables. On the regular branch, four scalar-normalization-invariant holographic combinations admit a global rational inverse to the continuous reduced couplings. At fixed compactification dimension the map has maximal rank, while the curvature-anomaly sum reconstructs the higher-dimensional Gauss–Bonnet coefficient without sign ambiguity. Holographic response thus provides an explicit, overdetermined boundary fingerprint of the underlying string reduction.

Recently, it was demonstrated that the disagreement between lattice calculations and holographic models, regarding rotational effects in the quark-gluon plasma (QGP), occurs due to different choices of reference frames. While a static observer measures a confinement temperature that decreases with rotation, one in a co-rotating frame finds the opposite behavior. Both results are correct, and a comprehension of the frame-dependency of the critical temperature is a significant step in the description of the QGP under rotation. In this article, we generalize this previous holographic result by describing the plasma through the most general Myers-Perry black hole solution. This breaks the spherical symmetry present in the equal angular momentum case, considered before. As a consequence, the local temperature measured by a co-rotating observer has a non-trivial angular dependence: it can decrease, increase or even behave non-monotonically when rotational velocity increases.

Gang-Kim-Stubbs theory $\mathcal{T}_n$ — a pioneering 3d bulk description of $M(2n+3,2)$ Virasoro minimal model as $\mathcal{N}=4$ rank-0 superconformal field theory upon topological A-twist — is derived from the compactification of a pair of parallel M5-branes on lens space $L(2n+3,2)$ with a single vertex removed. From this perspective, we propose a family of 3d $\mathcal{N}=2$ abelian gauge theories arising from the punctured $L(2n+3,1)$ lens space whose infrared phases realize the unitary member in the Galois orbit of $M(2n+3,2)$ modular tensor category. We also conjecture self-mirror rank-0 fixed points from amphichirality condition of the lens space.