This paper overviews the information paradox, or "unitarity crisis," and a proposed resolution called nonviolent unitarization. It begins by examining the conflict of principles yielding the crisis, which can be phrased in terms of a "black hole theorem" which outlines how basic assumptions come into conflict. Proposed resolutions of the conflict, along with problems with them, are overviewed. The very important underlying question of localization of information and its role is discussed at some length, taking into account effects of perturbative gravity. The difficulty in finding a consistent scenario for black hole evolution strongly suggests new interactions on event horizon scales; a "minimal" set of assumptions about these are parameterized in nonviolent unitarization. Possible criticisms of this scenario, and some responses, are given. New interactions at event horizon scales potentially lead to observable effects, via gravitational wave or electromagnetic channels, which are briefly discussed. A possible origin of nonviolent unitarization effects from a more fundamental description of quantum gravity, and possible implications for such a description, are also briefly discussed.

Extended objects (defects) in Quantum Field Theory exhibit rich, nontrivial dynamics describing a variety of physical phenomena. These systems often involve strong coupling at long distances, where the bulk and defects interact, making analytical studies challenging. By carefully analyzing the behavior of bulk symmetries in the presence of defects, we uncover robust topological constraints on defect RG flows. Specifically, we introduce the notions of $\textit{defect anomalies}$ and $\textit{strongly symmetric defects}$, both of which are RG-invariant. Several known notions, such as higher-form symmetries, fractionalization, and projective lines, are revealed to be manifestations of defect anomalies, which also encompass novel phenomena and forbid trivial defect dynamics in the IR. Meanwhile, strongly symmetric defects are shown to remain coupled at low energies, imposing powerful dynamical constraints. We verify our findings through concrete examples: exactly solvable defect RG flows in (1+1)d Conformal Field Theories with strongly symmetric lines and a surface defect in (2+1)d scalar QED.

Several generalizations of Vershik-Kerov limit shape problem are motivated by topological string theory and supersymmetric gauge theory instanton count. In this paper specifically we study the circular and linear quiver theories. We also briefly discuss the double-elliptic generalization of the Vershik-Kerov problem, related to six dimensional gauge theory compactified on a torus, and to elliptic cohomology of the Hilbert scheme of points on a plane. We prove that the limit shape in that setting is governed by a genus two algebraic curve, suggesting unexpected dualities between the enumerative and equivariant parameters.

In chaotic quantum systems the spectral form factor exhibits a universal linear ramp and plateau structure with superimposed erratic oscillations. The mean signal and the statistics of the noise can be probed by the moments of the spectral form factor, also known as higher-point spectral form factors. We identify saddle points in the SYK model that describe the moments during the ramp region. Perturbative corrections around the saddle point indicate that SYK mimics random matrix statistics for the low order moments, while large deviations for the high order moments arise from fluctuations near the edge of the spectrum. The leading correction scales inversely with the number of random parameters in the SYK Hamiltonian and is amplified in a sparsified version of the SYK model, which we study numerically, even in regimes where a linear ramp persists. Finally, we study the $q=2$ SYK model, whose spectral form factor exhibits an exponential ramp with increased noise. These findings reveal how deviations from random matrix universality arise in disordered systems and motivate their interpretation from a bulk gravitational perspective.

In the framework of AdS/CFT duality, we consider the semiclassical problem in general quadratic theory of gravity. We construct asymptotically global AdS and hyperbolic~(topological) AdS black hole solutions with non-trivial quantum hair in $4$ and $5$-dimensions by perturbing the maximally symmetric AdS solutions to the holographic semiclassical equations. We find that under certain conditions, our semiclassical solution of hyperbolic AdS black holes can be dynamically unstable against linear perturbations. In this holographic semiclassical context, we also study the thermodynamic instability of the hairy solutions in the $5$-dimensional Gauss-Bonnet theory by computing the free energy and show that depending on the parameter of the Gauss-Bonnet theory, the free energy can be smaller than that of the background maximally symmetric AdS solution in both the global AdS and hyperbolic AdS black hole cases.

We solve the Schr\"odinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the probability density of the scalar. Unlike related calculations for condensates of ultralight dark matter or boson stars, no assumption of spherical symmetry is made for the effective gravitational potential. Instead, the potential has only axial symmetry, consistent with the axial symmetry of the particle's probability density for eigenstates of $L_z$. With total angular momentum no longer a good quantum number, there are in general contributions from a range of partial waves. This permits us to study the partial-wave content of self-consistent solutions of the Schr\"odinger-Newton system.

We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised States (CLSs), which appear naturally by demanding $\textit{supertranslation}$ invariance of the system. We use CLS basis states, with inherent $\textit{ultra-local}$ correlations, to write down an interacting theory which shows a non-trivial phase structure and an emergent Carroll conformal symmetry at the gapless points. We analyze this theory in detail for both zero and finite chemical potential.

The formation of composite solitons produced by scalar fields without thermal phase transitions in the early Universe is considered. We present numerical simulations of the formation and evolution of soliton structures at the post-inflationary stage. The realistic initial conditions are obtained through the simulation of multiple quantum fluctuations during the inflation epoch. The initial field distributions allow to form local soliton clusters in the early Universe without the need for the thermal production of a soliton network throughout the Universe. We find that in three-dimensional space, the nontrivial composite field structures are formed in the form of <>, consisting of closed domain walls, domain walls bounded by cosmic strings, and scalar field radiation. The possible cosmological implications of the soliton foam are discussed.

We investigate the mutual relations between the centers of different elements in the deconstruction lattice of a 2D conformal model, and show how these can be described using exact sequences of abelian groups. In particular, we exhibit a long exact sequence connecting the centers of higher central quotients.

In arXiv:2310.17536, two of the authors studied the function $\mathscr{S}_{\boldsymbol{m}} = S_{\boldsymbol{m}} - \pi \sum_{i=1}^n (m_i - \tfrac{1}{m_i}) \log \mathsf{h}_{i}$ for orbifold Riemann surfaces of signature $(g;m_1,...,m_{n_e};n_p)$ on the generalized Schottky space $\mathfrak{S}_{g,n}(\boldsymbol{m})$. In this paper, we prove the holographic duality between $\mathscr{S}_{\boldsymbol{m}}$ and the renormalized hyperbolic volume $V_{\text{ren}}$ of the corresponding Schottky 3-orbifolds with lines of conical singularity that reach the conformal boundary. In case of the classical Liouville action on $\mathfrak{S}_{g}$ and $\mathfrak{S}_{g,n}(\boldsymbol{\infty})$, the holography principle was proved in arXiv:0005106 and arXiv:1508.02102, respectively. Our result implies that $V_{\text{ren}}$ acts as K\"ahler potential for a particular combination of the Weil-Petersson and Takhtajan-Zograf metrics that appears in the local index theorem for orbifold Riemann surfaces arXiv:1701.00771. Moreover, we demonstrate that under the conformal transformations, the change of function $\mathscr{S}_{\boldsymbol{m}}$ is equivalent to the Polyakov anomaly, which indicates that the function $\mathscr{S}_{\boldsymbol{m}}$ is a consistent height function with a unique hyperbolic solution. Consequently, the associated renormalized hyperbolic volume $V_{\text{ren}}$ also admits a Polyakov anomaly formula. The method we used to establish this equivalence may provide an alternative approach to derive the renormalized Polyakov anomaly for Riemann surfaces with punctures (cusps), as described in arXiv:0909.0807.

We revisit and extend the construction of six-dimensional orientifolds built upon the $T^4/\mathbb{Z}_N$ orbifolds with a non-vanishing Kalb-Ramond background, both in the presence of $\mathcal{N}=(1,0)$ supersymmetry and Brane Supersymmetry Breaking, thus amending some statements present in the literature. In the $N=2$ case, we show how the gauge groups on unoriented D9 and D5 (anti-)branes do not need to be correlated, but can be independently chosen complex or real. For $N>2$ we find that the Diophantine tadpole conditions severely constrain the vacua. Indeed, only the $N=4$ orbifold with a rank-two Kalb-Ramond background may admit integer solutions for the Chan-Paton multiplicities, if the $\mathbb{Z}_4$ fixed points support $\text{O}5_-$ planes, both with and without supersymmetry. All other cases would involve a fractional number of branes, which is clearly unacceptable. We check the consistency of the new $\mathbb{Z}_2$ and $\mathbb{Z}_4$ vacua by verifying the unitarity constraints for string defects coupled to Ramond-Ramond two-forms entering the Green-Schwarz-Sagnotti mechanism.

We generalize a recent ``AdS S-matrix" formulation for interacting massive scalars on AdS spacetimes to the case of massive vector fields. This method relies on taking the infinite radius limit for scattering processes perturbatively, which is analyzed using Witten diagrams in the momentum space formulation of global AdS with embedding space coordinates. It recovers the S-matrix with subleading corrections in powers of the inverse AdS radius about a flat spacetime region within the bulk. We first derive the massive vector bulk-to-boundary and bulk-to-bulk propagators within this perturbation theory. As an example, we consider the Abelian Higgs Model in a certain regime of the coupling parameter space to model an interacting Proca theory on AdS spacetimes. We specifically compute the AdS S-matrix for a process involving massive external vector fields mediated by a massive scalar. We lastly discuss possible massless limit of propagators within this perturbative framework.

We study the differential equations that follow from Yangian symmetry which was recently observed for a large class of conformal Feynman graphs, originating from integrable `fishnet' theories. We derive, for the first time, the explicit general form of these equations in the most useful conformal cross-ratio variables, valid for any spacetime dimension. This allows us to explore their properties in detail. In particular, we observe that for general Feynman graphs a large set of terms in the Yangian equations can be identified with famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators. We also show that for certain nontrivial graphs the relation with GKZ systems is exact, opening the way to using new powerful solution methods. As a side result, we also elucidate the constraints on the topology and parameter space of Feynman graphs stemming from Yangian invariance.

The combinatorics of dimer models on brane tilings describe a large class of four-dimensional $\mathcal{N}=1$ gauge theories that afford quiver descriptions and have toric moduli spaces. We introduce a combinatorial optimization method leveraging simulated annealing to explicitly construct geometrically consistent brane tilings, providing a proof of concept for efficient generation of gauge theories using metaheuristic techniques. The implementation of this idea recovers known examples and allows us to derive a new brane tiling with $26$ quantum fields, whose construction is beyond the computational power of current methods.

Recently proposed $SL(2,\mathbb{Z})$ invariant $\alpha$-attractor models have plateau potentials with respect to the inflaton and axion fields. The slope of the potential in the inflaton direction is exponentially suppressed at large values of the inflaton field, but the slope of the potential in the axion direction is double-exponentially suppressed. Therefore, the axion field remains nearly massless and practically does not change during inflation. The inflationary trajectory in such models is stable with respect to quantum fluctuations of the axion field. We show that isocurvature perturbations do not feed into the curvature perturbations during inflation, and argue that such transfer may remain inefficient at the post-inflationary stage.

We compute the entanglement entropy of an interval for a chiral scalar on a circle at an arbitrary temperature. We use the resolvent method, which involves expressing the entropy in terms of the resolvent of a certain operator, and we compute that resolvent by solving a problem that entails finding an analytic function on the complex torus with certain jump conditions at the interval. The resolvent is relevant by itself, since it can be used to compute any function of the reduced density matrix. We illustrate that by also computing all the R\'enyi entropies for the model.

Recently obtained black hole solutions within the framework of beyond-Horndeski theories, which have the advantage of featuring primary hair, are generalized in the presence of two axionic fields. In order to induce a momentum dissipation, the axionic field solutions are homogeneously distributed along the horizon coordinates of the planar base manifold. We show that, despite the explicit dependence of the scalar field and the metric on the primary hair, this latter does not directly affect the calculation of transport properties. Its influence is indirect, modifying the horizon location, but the transport properties themselves do not explicitly depend on the hair parameter. We take a step further and show that even within a more general class of beyond-Horndeski theories, where the scalar field depends linearly on the hair parameter, the scalar hair still has no direct impact on the DC conductivity. This result underscores the robustness of our earlier findings, and seem to confirm that the transport properties remain unaffected by the explicit presence of the hair parameter.

The recently proposed dark dimension scenario reveals that the axions can be localized on the Standard Model brane, thereby predicting the quantum chromodynamics (QCD) axion decay constant from the weak gravity conjecture: $f_a\lesssim M_5 \sim 10^{9}-10^{10}\, \rm GeV$, where $M_5$ is the five-dimensional Planck mass. When combined with observational lower bounds, this implies that $f_a$ falls within a narrow range $f_a\sim 10^{9}-10^{10}\, \rm GeV$, corresponding to the axion mass $m_a\sim 10^{-3}-10^{-2}\, \rm eV$. At this scale, the QCD axion constitutes a minor fraction of the total cold dark matter (DM) density $\sim 10^{-3}-10^{-2}$. In this work, we investigate the issue of QCD axion DM within the context of the dark dimension and demonstrate that the QCD axion in this scenario can account for the entire DM abundance through a simple two-axion mixing mechanism. Here we consider the resonant conversion of an axion-like particle (ALP) into a QCD axion. We find that, in a scenario where the ALP possesses a mass of approximately $m_A \sim 10^{-5} \, \rm eV$ and a decay constant of $f_A \sim 10^{11} \, \rm GeV$, the QCD axion in the dark dimension scenario can account for the overall DM.

We show that the Mathieu groups $M_{24}$ and $M_{23}$ in the isometry group of the odd Leech lattice do not lift to subgroups of the automorphism group of its lattice vertex operator (super)algebra. In other words, the subgroups $2^{24}.M_{24}$ and $2^{23}.M_{23}$ of the automorphism group of the odd Leech lattice vertex operator algebra are non-split extensions. Our method can also confirm a similar result for the Conway group $\mathrm{Co}_0$ and the Leech lattice, which was already shown in [Griess 1973]. This study is motivated by the moonshine-type observation on the $\mathcal{N}=2$ extremal elliptic genus of central charge 24 by [Benjamin, Dyer, Fitzpatrick, Kachru arXiv:1507.00004]. We also investigate weight-1 and weight-$\frac{3}{2}$ currents invariant under the subgroup $2^{24}.M_{24}$ or $2^{23}.M_{23}$ of the automorphism group of the odd Leech lattice vertex operator algebra, and revisit an $\mathcal{N}=2$ superconformal algebra in it.

We study oscillons in a real scalar field theory in a (3+1)-dimensional AdS space with global coordinates. The initial configuration is given by a Gaussian shape with an appropriate core size as in Minkowski spacetime. The solution exhibits a long lifetime. In particular, since the AdS space can be seen as a box, the recurrence phenomenon can be observed under suitable conditions. Finally, we discuss some potential applications of the oscillon in the context of AdS/CFT duality.

Motivated by phenomenology of myriad recently-identified topologically non-trivial phases of matter, we introduce effective field theories (EFTs) for the quantum skyrmion Hall effect (QSkHE). We employ a single, unifying generalisation for this purpose: in essence, a lowest Landau level projection defining a non-commutative, fuzzy sphere with position coordinates proportional to SU(2) generators of matrix representation size $N\times N$, may host an intrinsically 2+1 dimensional, topologically non-trivial many-body state for small $N$ as well as large $N$. That is, isospin degrees of freedom associated with a matrix Lie algebra with $N \times N$ generators potentially encode some finite number of spatial dimensions for $N\ge 2$, a regime in which isospin has previously been treated as a label. This statement extends to more general $p$-branes subjected to severe fuzzification as well as membranes. As a consequence of this generalisation, systems with $d$ Cartesian spatial coordinates and isospin degrees of freedom encoding an additional $\delta$ fuzzy coset space coordinates can realise topologically non-trivial states of intrinsic dimensionality up to $d$+$\delta$+1. We therefore identify gauge theories with extra fuzzy dimensions generalised to retain dependence upon gauge fields over fuzzy coset spaces even for severe fuzzification (small $N$), as EFTs for the QSkHE. We furthermore generalise these EFTs to space manifolds with local product structure exploiting the dimensional hierarchy of (fuzzy) spheres. For this purpose, we introduce methods of anisotropic fuzzification and propose formulating topological invariants on fuzzy coset spaces as artifacts of projecting matrix Lie algebras to occupied subspaces. Importantly, we focus on phenomenology indicating the 2+1 D SU(2) gauge theory should be generalised using this machinery, and serves as a minimal EFT of the QSkHE.

We study gauging operations (or group extensions) in (smeared) boundary conformal field theories (BCFTs) and bulk conformal field theories and their applications to various phenomena in topologically ordered systems. We apply the resultant theories to the correspondence between the renormalization group (RG) flow of CFTs and the classification of topological quantum field theories in the testable information of general classes of partition functions. One can obtain the bulk topological properties of $2+1$ dimensional topological ordered phase corresponding to the massive RG flow of $1+1$ dimensional systems, or smeared BCFT. We present an obstruction of mass condensation for smeared BCFT analogous to the Lieb-Shultz-Mattis theorem for noninvertible symmetry. Related to the bulk topological degeneracies in $2+1$ dimensions and quantum phases in $1+1$ dimensions we construct a new series of BCFT. We also investigate the implications of the massless RG flow of $1+1$ dimensional CFT to $2+1$ dimensional topological order which corresponds to the earlier proposal by L. Kong and H. Zheng in [Nucl. Phys. B 966 (2021), 115384], arXiv:1912.01760 closely related to the integer-spin simple current by Schellekens and Gato-Rivera. We study the properties of the product of two CFTs connected by the two kinds of massless flows. The (mock) modular covariants appearing in the analysis seem to contain new ones. By applying the folding trick to the coupled model, we provide a general method to solve the gapped and charged domain wall. One can obtain the general phenomenology of the transportation of anyons through the domain wall. Our work gives a unified direction for the future theoretical and numerical studies of the topological phase based on the established data of classifications of conformal field theories or modular invariants.

The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of $t$. It provides an alternative definition of Macdonald theory. We discuss lifting the triad to an elliptic generalization of the Noumi-Shiraishi functions. The central unknown ingredient is linear equations, for which we discuss various possible approaches, including immediate elliptic deformation of periodicity conditions, (elliptic) Ding-Iohara-Miki algebra operators, and elliptic Kostka coefficients.

General Relativity famously predicts precession of orbital motions in the Schwarzschild metric. In this paper we show that by adding a NUT charge $N = iM$ the precession vanishes to all orders in $G$ even for rotating black holes. Moreover, we conjecture a generalization of the eikonal formula and show that the classical integrable trajectories determine the full quantum amplitude for this black hole, by means of exponentiation of the Post-Minkowskian radial action. Several consequences of integrability in self-dual gravity are discussed.

We propose a new ``universal expansion" for one-loop amplitudes with arbitrary number of gluons in $D$ dimensions, which holds for general gauge theories with gluons/fermions/scalars in the loop, including pure and supersymmetric Yang-Mills theories. It expresses the $n$-gluon amplitudes as a linear combination of universal scalar-loop amplitudes with $n{-}m$ gluons and $m$ scalars, multiplied by gauge-invariant building blocks (defined for general gauge theories); the integrands of these scalar-loop amplitudes are given in terms of tree-level objects attached to the scalar loop, or by differential operators acting on the most important part which is proportional to $D$ (with $m=0$). We present closed-formula for these one-loop integrands and prove them by showing that the single cuts are correctly reproduced by the gluing of an additional pair of gluons (fermions/scalars) in the forward limit, plus $n$ gluons in a tree amplitude.

We calculate n-point hard string scattering amplitudes (HSSA) with n-2 tachyons and 2 tensor states at arbitrary mass levels. We discover the stringy scaling behavior of these HSSA. It is found that for HSSA with more than 2 transverse directions, the degree of stringy scaling dimM2 decreases comparing to the degree of stringy scaling dimM1 of the n-1 tachyons and 1 tensor HSSA calculated previously. Moreover, we propose a set of K-identities which is the key to demonstrate the stringy scaling behavior of HSSA. We explicitly prove both the diagonal and off-diagonal K-identities for the 4-point HSSA and give numerical proofs of these K-identities for some higher point HSSA.

A realization of gravitational amplitudes based in the large $N$ limit of a certain 2d $SU(N)$ Kac-Moody theory has been recently proposed. We relate this proposal to Color Kinematics (CK) duality and present an extension to EFT amplitudes for matter particles with any mass and spin. In particular, we recast these EFT amplitudes as celestial correlation functions and show they posses a chiral $w_{1+\infty}$ symmetry algebra if they are minimally coupled in the bulk. Massive states lead to an off-shell 1-parameter deformation of the algebra. Finally, we argue that in the limit $S\to\infty$ these states correspond to the Kerr black hole and we rediscover a classical $w_{1+\infty}$ action of Penrose.

We study the representation theory of the spherical double affine Hecke algebra (DAHA) of $C^\vee C_1$, using brane quantization. By showing a one-to-one correspondence between Lagrangian $A$-branes with compact support and finite-dimensional representations of the spherical DAHA, we provide evidence of derived equivalence between the $A$-brane category of $\mathrm{SL}(2,\mathbb{C})$-character variety of a four-punctured sphere and the representation category of DAHA of $C^\vee C_1$. The $D_4$ root system plays an essential role in understanding both the geometry and representation theory. In particular, this $A$-model approach reveals the action of an affine braid group of type $D_4$ on the category. As a by-product, our geometric investigation offers detailed information about the low-energy dynamics of the SU(2) $N_f=4$ Seiberg-Witten theory.

A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum $N\to \infty$ limit. At finite $N$ the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied $w_{1+\infty}$ hierarchy of soft currents and its realization from a sigma model in twistor space.

We revisit the instanton partition function for 5d $\mathcal{N}=1$ SO($N$) gauge theories compactified on S$^1$, computed from the topological vertex formalism with the O-vertex based on a 5-brane web diagram with an O5-plane. We introduce an identity that enables us to rewrite the unrefined partition function into a new expression in terms of the Nekrasov factors summed over Young diagrams, which can be interpreted as the freezing of an O7-plane. Based on this, we propose topological vertex formalism with an O7$^+$-plane.

The spectral form factor is believed to provide a special type of behavior called "dip-ramp-plateau" in chaotic quantum systems which originates from the random matrix theory. A similar behavior could be observed for deterministic systems, ranging from the Riemann zeta function to the scattering amplitudes of different types. It has been shown recently, the same behavior is observed for the spectral form factor when the normal modes of a scalar massless field theory in the brickwall model of the BTZ black hole are substituted as eigenvalues of some quantum Hamiltonian. At the same time, the level spacing distribution of these eigenvalues differs from that associated with the random matrix theory ensembles. In this paper, we generalize these results considering the recently proposed generalized spectral form factor for the de Sitter and BTZ spacetimes. We study the details of this complex-valued form factor for integrable quantum systems and for backgrounds with a horizon comparing it with the random matrix theory behavior. As a result, we confirm that the scalar field normal modes once again exhibit features of chaos.

We study mixed state entanglement measures in a higher dimensional $T\bar{T}$ deformed field theory at finite temperature. The holographic dual is described by AdS$_{d+1}$ black brane geometry with a finite cut-off. We compute the entanglement wedge cross section (EWCS), proposed to be dual to entanglement of purification (EoP) and holographic entanglement negativity (HEN) for strip like subsystems. The behavior of EWCS and HEN is studied across different regimes of temperature and deformation parameter. It is observed that the deformation and temperature exhibit similar effects on these two entanglement measures. Increasing the deformation leads to a decrease in the entanglement between the subsystems.

We perform a detailed study of the gravitational tidal Love numbers of extremal zero-temperature Kerr black holes. These coefficients are finite and exhibit the dissipative nature of these maximally spinning black holes. Upon considering the dynamical behavior of the tidal deformations of the extremal Kerr black holes, we provide explicit expressions of the Love numbers at low frequencies. Their calculation is simplified to specific formulas, which are directly derived using the Leaver-MST methods.

We perform the Becchi-Rouet-Stora-Tyutin (BRST) quantization of a (0 + 1)-dimensional non-interacting cosmological Friedmann-Robertson-Walker (FRW) model. This quantization leverages the classical infinitesimal and continuous reparameterization symmetry transformations of the system. To derive the nilpotent reparameterization invariant (anti-)BRST symmetry transformations for the scale factor and corresponding momentum variables of the FRW model, we employ the modified Bonora-Tonin supervariable approach (MBTSA) to BRST formalism. Through this approach, we also establish the (anti-)BRST invariant Curci-Ferrari (CF)-type restriction for this cosmological reparameterization invariant model. Further, we obtain the nilpotent (anti-)BRST symmetry transformations for other variables within the model using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of ACSA, the CF-type restriction is demonstrated through two key aspects: (i) the invariance of the coupled Lagrangians under symmetry transformations, and (ii) the absolute anticommutativity of the conserved (anti-)BRST charges. Notably, applying the MBTSA to a physical cosmological system, specifically a one-dimensional one, constitutes a novel contribution to this work. Additionally, in the application of ACSA, we restrict our analysis to (anti-)chiral super expansions of supervariables, leading to the unique observation of the absolute anticommutativity of the (anti-)BRST charges. Moreover, we highlight that the CF-type restriction demonstrates a universal nature, remaining consistent across any reparameterization invariant models in D-dimensional spacetime.

Regimes of Lorentz-violating effective field theories are studied in which departures from Lorentz symmetry are nonperturbative. Within a free toy theory exhibiting Lorentz breakdown involving an operator of mass dimension three, it is shown that conventional methods suffice to achieve field quantization and Fock-space construction. However, the absence of an observer-invariant energy-positivity condition requires physical input beyond the free theory for the unambiguous identification of a ground state. An investigation of the role of thermodynamics in this context is instigated.

In nature, some UV features of the dynamics are reflected in IR quantities. In fully relativistic theories, this connection can be probed through the analyticity properties of scattering amplitudes, allowing to understand which IR theories respect the UV assumptions of quantum field theory. The ensuing analyticity bounds can be usually rephrased as the absence of faster-than-light propagation for low-energy excitations. While it is interesting to understand these relations and their IR characterization for theories that have less idealized properties, it is also more difficult to derive analyticity bounds in these cases. For theories that spontaneously break Lorentz symmetry, recent progress was made by considering correlators of conserved currents and their analyticity properties. In this work, we focus on such theories and close the gap from the IR side, deriving bounds from the speed of propagation that are equivalent to the known analyticity bounds. Our bounds require that gapped excitations have a slower speed than gapless ones, at least for momenta that are low with respect to the mass gap. These results suggest a way to study the UV/IR connection in more complex theories.

Obtaining the classification of 3d $\mathcal{N}=4$ quivers whose Coulomb branches have an isolated singularity is an essential step in understanding moduli spaces of vacua of supersymmetric field theories with 8 supercharges in any dimension. In this work, we derive a full classification for such Abelian quivers with arbitrary charges, and identify all possible Coulomb branch geometries as quotients of $\mathbb{H}^n$ by $\mathrm{U}(1)$ or a finite cyclic group. We give two proofs, one which uses the decay and fission algorithm, and another one relying only on explicit computations involving 3d mirror symmetry. In the process, we put forward a method for computing the 3d mirror of any $\mathrm{U}(1)^r$ gauge theory, which is sensitive to discrete gauge factors in the mirror theory. This constitutes a confirmation for the decay and fission algorithm.

Ever since Yau's non-constructive existence proof of Ricci-flat metrics on Calabi-Yau manifolds, finding their explicit construction remains a major obstacle to development of both string theory and algebraic geometry. Recent computational approaches employ machine learning to create novel neural representations for approximating these metrics, offering high accuracy but limited interpretability. In this paper, we analyse machine learning approximations to flat metrics of Fermat Calabi-Yau n-folds and some of their one-parameter deformations in three dimensions in order to discover their new properties. We formalise cases in which the flat metric has more symmetries than the underlying manifold, and prove that these symmetries imply that the flat metric admits a surprisingly compact representation for certain choices of complex structure moduli. We show that such symmetries uniquely determine the flat metric on certain loci, for which we present an analytic form. We also incorporate our theoretical results into neural networks to achieve state-of-the-art reductions in Ricci curvature for multiple Calabi-Yau manifolds. We conclude by distilling the ML models to obtain for the first time closed form expressions for Kahler metrics with near-zero scalar curvature.

We study solutions of the Wheeler DeWitt (WdW) equation in order to recover standard results of cosmological perturbation theory. In mini-superspace, we introduce a dimensionless gravitational coupling $\alpha$ that is typically very small and functions like $\hbar$ in a WKB expansion. We seek solutions of the form $\Psi = e^{iS/\alpha} \psi$ that are the closest quantum analog of a given classical background spacetime. The function $S$ satisfies the Hamilton-Jacobi equation, while $\psi$ obeys a Schr\"odinger-like equation and has a clear probabilistic interpretation. By using the semiclassical limit we express the relation between $\psi$ and the wavefunction of the universe in perturbation theory, $\psi_P$. We apply our formalism to two main examples. The first is a scalar field with a purely exponential potential, of which particularly simple, scaling solutions are known. The other is a slow-roll scenario expanded in the vicinity of the origin in field space. We discuss possible deviations from the classical background trajectory as well as the higher ``time" derivative terms that are present in the WdW equation but not in the perturbative approach. We clarify the conditional probability content of the wavefunctions and how this is related with the standard gauge fixing procedure in perturbation theory.

We consider four-point functions of protected, double- and single-trace operators in the large central charge limit. We use superconformal symmetry to disentangle the contribution of protected operators in the partial wave decomposition. With this information, we fix the non protected part of such correlators up to subleading order in the large central charge expansion. We particularly focus on the triple-trace sector of the correlator and comment on the connection to the holographic description of these correlators.

We examine Friedmann-Lema\^itre-Robertson-Walker cosmology, incorporating quantum gravitational corrections through the functional renormalization group flow of the effective action for gravity. We solve the Einstein equation with quantum improved coupling perturbatively including the case with non-vanishing classical cosmological constant (CC) which was overlooked in the literatures. We discuss what is the suitable identification of the momentum cutoff $k$ with time scale, and find that the choice of the Hubble parameter is suitable for vanishing CC but not so for non-vanishing CC. We suggest suitable identification in this case. The energy-scale dependent running coupling breaks the time translation symmetry and then introduces a new physical scale.

STRINGS is a Monte Carlo (MC) event generator for simulating the production and decay of first and second string resonances in proton-proton collisions. STRINGS can also interface with other programs such as Pythia using the Les Houches Accord to produce more accurate data. In this paper, we validate STRINGS for the simulation of 2-parton $\rightarrow$ $\gamma$-parton scattering events by comparing to previous literature. After validation, we produce MC samples of resonances using $M_s$ = {5.0,5.5,6.0,6.5,7.0} TeV at $\sqrt{s}$ = {13,13.6} TeV with STRINGS and Pythia and analyze the kinematic data. To accurately reproduce previous results close to resonance, it is necessary to introduce a scaling factor of $\approx$ 0.53. With this correction, the resonance structure is as expected.

We investigate the (axial) quasinormal modes of black holes embedded in generic matter profiles. Our results reveal that the axial QNMs experience a redshift when the black hole is surrounded by various matter environments, proportional to the compactness of the matter halo. Our calculations demonstrate that for static black holes embedded in galactic matter distributions, there exists a universal relation between the matter environment and the redshifted vacuum quasinormal modes. In particular, for dilute environments the leading order effect is a redshift $1+U$ of frequencies and damping times, with $U \sim -{\cal C}$ the Newtonian potential of the environment at its center, which scales with its compactness ${\cal C}$.

Because of their weak interactions with the strongly interacting matter produced in relativistic heavy-ion collisions, dileptons provide an ideal probe of the early dynamics of these collisions. Here, we study dilepton production using a partonic transport model that is based on an extended Nambu-Jona-Lasinio (NJL) model. In this model, the in-medium quark masses decrease with increasing temperature as a result of the restoration of chiral symmetry. We find that the extracted temperature from dileptons of intermediate masses agrees well with the temperature of the partonic matter, suggesting that dilepton production can be used as a thermometer for the produced partonic matter. Our results also indicate that the extracted in-medium quark masses decrease with increasing dilepton temperature, implying that dilepton production can further serve as a probe of chiral symmetry restoration in high energy heavy-ion collisions.

Employing the recently developed open quantum system Effective Field Theory framework, we investigate jet production and evolution in a dense nuclear medium in electron-ion/heavy-ion collisions. We confirm that the frequent monitoring of the jet by the medium leads to the emergence of a perturbative transverse momentum scale, often referred to as the saturation scale that necessitates further factorization to completely isolate the non-perturbative physics of the medium. A part of this goal is achieved in this paper by providing an operator definition for the broadening probability of a gluon in the medium within the Markovian approximations. We show that this distribution is (semi)universal; it depends on the angular measurement on the jet and probes both the large and small $x$ dynamics of the medium. We further elucidate all other contributions to non-perturbative physics suggesting that the parameterization of non-perturbative physics is more complex than previously assumed and outline steps required for a complete factorization of the jet production cross section.

Effective String Theory (EST) is a powerful tool used to study confinement in pure gauge theories by modeling the confining flux tube connecting a static quark-anti-quark pair as a thin vibrating string. Recently, flow-based samplers have been applied as an efficient numerical method to study EST regularized on the lattice, opening the route to study observables previously inaccessible to standard analytical methods. Flow-based samplers are a class of algorithms based on Normalizing Flows (NFs), deep generative models recently proposed as a promising alternative to traditional Markov Chain Monte Carlo methods in lattice field theory calculations. By combining NF layers with out-of-equilibrium stochastic updates, we obtain Stochastic Normalizing Flows (SNFs), a scalable class of machine learning algorithms that can be explained in terms of stochastic thermodynamics. In this contribution, we outline EST and SNFs, and report some numerical results for the shape of the flux tube.

In this paper, we present an algorithm to generate the collider events of the GeV-scale oscillating sterile neutrinos with the ready-made event generation tools in the case that the crossing-widths among the nearly-degenerate fermionic fields arise. We prove the validity of our algorithm, and adopt some tricks for practical calculations. The formulations of the particle oscillation processes are also improved in the framework of the quantum field theory, offering us the ability to simulate the flying distances of the oscillating intermediate sterile neutrinos while regarding them as the internal lines in the Feynmann diagrams.

The semi-inclusive deep-inelastic scattering (SIDIS) process requires the presence of an identified hadron H$'$ in the final state, which arises from the scattering of a lepton with an initial hadron P. By employing factorization in quantum chromodynamics (QCD), SIDIS provides essential knowledge on the hadron structure, enabling the exploration of parton distribution functions (PDFs) and fragmentation functions (FFs). The coefficient functions for SIDIS can be calculated in perturbative QCD and are currently known to the next-to-next-to-leading order (NNLO) for the cases, where the incoming lepton and the hadron P are either both polarized or unpolarized. We present a detailed description of these NNLO computations, including a thorough discussion of all the partonic channels, the calculation of the amplitudes and master integrals for the phase-space integration as well as the renormalization of ultraviolet divergences and mass factorization of infrared divergences in dimensional regularization through NNLO. We provide an extensive phenomenological analysis of the effects of NNLO corrections on SIDIS cross sections for different PDFs and FFs and various kinematics, including those of the future Electron-Ion Collider (EIC). We find that these corrections are not only significant but also crucial for reducing the dependence on the renormalization and factorization scales $\mu_R$ and $\mu_F$ to obtain stable predictions.

We show that the mass of a self-interacting dark matter candidate, specifically a Dirac fermion, can be generated by composite dynamics, with a light scalar mediator emerging alongside the Higgs itself as composite particles. These novel models naturally explain the halo structure problems at various scales and alleviates the Standard Model naturalness problem simultaneously. The relic density of the dark matter candidates is particle anti-particle symmetric and due to thermal freeze-out. These models are four-dimensional gauge theories with a minimal number of fermions charged under a new confining gauge group. Finally, we demonstrate that these models satisfy various constraints set by the dark matter relic density, Big Bang Nucleosynthesis, Cosmic Microwave Background, as well as direct and indirect detection experiments.

Let $\Psi(\mathbb{z},\mathbb{a},q)$ be the fundamental solution matrix of the quantum difference equation in the equivariant quantum K-theory for Nakajima variety $X$. In this work, we prove that the operator $$ \Psi(\mathbb{z},\mathbb{a},q) \Psi\left(\mathbb{z}^p,\mathbb{a}^p,q^{p^2}\right)^{-1} $$ has no poles at the primitive complex $p$-th roots of unity $\zeta_p$ in the curve counting parameter $q$. As a byproduct, we show that the eigenvalues of the iterated product of the operators ${\bf M}_{\mathcal{L}}$ from the quantum difference equation on $X$ $$ {\bf M}_{\mathcal{L}} (\mathbb{z},\mathbb{a},q) {\bf M}_{\mathcal{L}} (\mathbb{z} q^{\mathcal{L}},\mathbb{a},q) \cdots {\bf M}_{\mathcal{L}} (\mathbb{z} q^{(p-1)\mathcal{L}},\mathbb{a},q) $$ evaluated at $\zeta_p$ are described by the Bethe equations for $X$ in which all variables are substituted by their $p$-th powers. Finally, upon a reduction of the quantum difference equation on $X$ to the quantum differential equation over the field with finite characteristic, the above iterated product transforms into a Grothendiek-Katz $p$-curvature of the corresponding differential connection whereas ${\bf M}_{\mathcal{L}} (\mathbb{z}^p,\mathbb{a}^p,q^p)$ becomes a certain Frobenius twist of that connection. In this way, we are reproducing, in part, the statement of a theorem by Etingof and Varchenko.

We consider the classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the complete gauge symmetry of these additional equations . The unfree variation of the trajectories reduces to the infinitesimal gauge symmetry transformation of the equations restricting the trajectories. We explicitly derive the equations that follow from the requirement that this gauge variation of the action vanishes. The system of equations for conditional extrema is not Lagrangian as such, but it admits an equivalent Hamiltonian formulation with a non-canonical Poisson bracket. The bracket is degenerate, in general. Alternatively, the equations restricting dynamics could be added to the action with Lagrange multipliers with unrestricted variation of the original variables. In this case, we would arrive at the Lagrangian equations for original variables involving Lagrange multipliers and for Lagrange multipliers themselves. In general, these two methods are not equivalent because the multipliers can bring extra degrees of freedom compared to the case of equations derived by unfree variation of the action. We illustrate the general method with two examples. The first example is the particle in central field with varying trajectories restricted by equation of conservation of angular momentum. The phase space gets one more dimension, and there is an extra conserved quantity $K$ which is responsible for precession of trajectories. $K=0$ corresponds to the trajectories of usual Lagrangian dynamics. The second example is the linearized gravity with Einstein-Hilbert action and the class of varying fields is restricted by linearized Nordstr\"om equation. This conditional extrema problem is shown to lead to the linearized Cotton gravity equations.

We study the transition rates of an atom rotating in a circular orbit, which is coupled with fluctuating electromagnetic fields in vacuum. We find that when the rotational angular velocity exceeds the transition frequency of the atom, the excitation rate can reach the same order of magnitude as the emission rate, even with an extremely low centripetal acceleration resulting from a very small orbital radius. For experimentally accessible centripetal accelerations, the excitation rate of centripetally accelerated atoms can be up to ten to the power of two hundred thousand times that of linearly accelerated atoms with the same acceleration. Our result suggests that the circular version of the Unruh effect can be significant even at very small centripetal accelerations, contrary to the common belief that a large Unruh effect requires large acceleration. This finding sheds new light on the experimental detection of the circular Unruh effect.

We study how a charged particle moving in a uniform magnetic field along its standard circular path (cyclotron motion) reacts to a short-duration, homogeneous, uniform electric field pulse injected in the plane perpendicular to the magnetic field. A `permanent' change in the radius of the initial circle and a shift of its centre is noted at later times, after the pulse is switched off. The magnitude of the velocity undergoes a change too, akin to a `velocity kick'. In summary, our results suggest a pulse-induced `electromagnetic memory-like effect', which is not quite a `wave memory', but, nevertheless, has similar features within a simple, non-relativistic context.

Ho\v{r}ava-Lifshitz gravity (to be precise, its projectable version) is recognized as a renormalizable, unitary, and asymptotically free quantum field theory of gravity. Notably, one of its cosmological predictions is that it can produce scale-invariant primordial density fluctuations and primordial gravitational waves without relying on inflation. In this paper, we investigate the quantum nature of the primordial gravitational waves generated in Ho\v{r}ava-Lifshitz gravity. It has been suggested that, for some inflationary models, the non-classicality of primordial gravitational waves in the squeezed coherent quantum state can be detected using the Hanbury Brown - Twiss (HBT) interferometry. We show that in Ho\v{r}ava-Lifshitz gravity, scale-invariant primordial gravitational waves can be generated during both the radiation-dominated and matter-dominated eras of the Universe. Moreover, the frequency range of their quantum signatures is shown to extend beyond that of inflationary models.

The algebra of exterior differential forms on a regular 3-Sasakian 7-manifold is investigated, with special reference to nearly-parallel $G_2$ 3-forms. This is applied to the study of 3-forms invariant under cohomogeneity-one actions by $SO(4)$ on the 7-sphere and on Berger's space $SO(5)/SO(3)$.

Given recent discovery of the quantum skyrmion Hall effect, we re-examine the related canonical Bernevig-Hughes-Zhang (BHZ) model for the quantum spin Hall insulator. Within the framework of the quantum skyrmion Hall effect, isospin degree(s) of freedom of the BHZ model encode additional spatial dimensions. Consistent with this framework, we observe phenomena similar to those of the four dimensional Chern insulator, revealed by weakly breaking time-reversal symmetry. Bulk-boundary correspondence of these states includes real-space boundary orbital angular momentum textures and gapless boundary modes that are robust against magnetic disorder, consistent with compactified three dimensional boundary Weyl nodes (WN$_F$s) of the quantum skyrmion Hall effect. These theoretical findings are furthermore consistent with past experimental work reporting unexpected edge conduction in HgTe quantum wells under applied Zeeman and orbital magnetic fields. This past work is therefore potentially the first known experimental observation of signatures of the quantum skyrmion Hall effect beyond the quantum Hall effect.

In this study, we explore how a non-minimal coupling between dark matter and gravity can affect the behavior of dark matter in galaxy clusters. We have considered the case of a disformal coupling, which leads to a modification of the Poisson equation. Building on an earlier work, we expand the analysis considering all possible disformal coupling scenarios and employing various dark matter density profiles. In doing so, we aim to constrain the key parameter in our model, the characteristic coupling length. To achieve this, we analyze data from a combination of strong and weak lensing using three statistical approaches: a single cluster fitting procedure, a joint analysis, and one with stacked profiles. Our findings show that the coupling length is typically very small, thus being fully consistent with general relativity, although with an upper limit at $1\sigma$ which is of the order of $100$ kpc.

We present new examples of superintegrable matrix/eigenvalue models. These examples arise as a result of the exploration of the relationship between the theory of superintegrability and multivariate orthogonal polynomials. The new superintegrable examples are built upon the multivariate generalizations of the Meixner-Pollaczek and Wilson polynomials and their respective measures. From the perspective of multivariate orthogonal polynomials in this work we propose expressions for (generalized) moments of the respective multi-variable measures. From the perspective of superintegrability we uncover a couple of new phenomena such as the deviation from Schur polynomials as the superintegrable basis without any deformation and new combinatorial structures appearing in the answers.

We explicitly establish that the Kerr metric represents a pair of self-dual and anti-self-dual gravitational dyons (Taub-NUT instantons). We show that the Newman-Janis algorithm precisely originates from this fact. More generally, this program of understanding four-dimensional black holes as systems of chiral dyons extends to Kerr-Newman and Kerr-Taub-NUT solutions as well.

Modifications of standard general relativity that bring torsion into a game have a long-standing history. However, no convincing arguments exist for or against its presence in physically acceptable gravity models. In this Letter, we provide an argument based on spectral geometry (using methods of pseudo-differential calculus) that suggests that the torsion shall be excluded from the consideration. We demonstrate that there is no well-defined functional extending to the torsion-full case of the spectral formulation of the Einstein tensor.

We propose a (1+1)D lattice model, inspired by a weak Hopf algebra generalization of the cluster state model, which realizes Haagerup fusion category symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra $H_3$ from the Haagerup fusion category, ensuring that the representation category of $H_3$ is equivalent to Haagerup fusion category. Utilizing the framework of symmetry topological field theory (SymTFT), we develop an ultra-thin weak Hopf quantum double model, characterized by a smooth topological boundary condition. We show that this model supports Haagerup fusion category symmetry. Finally, we solve the ground state of the model in terms of a weak Hopf matrix product state, which serves as a natural generalization of the cluster state, embodying Haagerup fusion category symmetry.

Minimal dark matter is an attractive candidate for dark matter because it is stabilized without the need to impose additional symmetries. It is known that the mass of the $SU(2)_L$ quintuplet fermion dark matter is predicted to be around 14 TeV, based on the thermal production mechanism. In this work, we embed the quintuplet dark matter within non-supersymmetric $SU(5)$ grand unified theories. We find that two pairs of colored sextet fermions are required at the $\mathcal{O}(1-10)~\mathrm{TeV}$ scale to achieve gauge coupling unification, with the unification scale near the reduced Planck scale. These colored sextet fermions become metastable because their interactions are suppressed by the unification scale. Our model can be tested through comprehensive searches for colored sextet fermions in collider experiments, as well as through indirect and direct detection methods for minimal dark matter.

We test the standardizability of a homogeneous sample of 41 lower-redshift ($0.00415\leq z \leq 0.474$) active galactic nuclei (AGNs) reverberation-mapped (RM) using the broad H$\alpha$ and H$\beta$ emission lines. We find that these sources can be standardized using four radius$-$luminosity ($R-L$) relations incorporating H$\alpha$ and H$\beta$ time delays and monochromatic and broad H$\alpha$ luminosities. Although the $R-L$ relation parameters are well constrained and independent of the six cosmological models considered, the resulting cosmological constraints are weak. The measured $R-L$ relations exhibit slightly steeper slopes than predicted by a simple photoionization model and steeper than those from previous higher-redshift H$\beta$ analyses based on larger datasets. These differences likely reflect the absence of high-accreting sources in our smaller, lower-redshift sample, which primarily comprises lower-accreting AGNs. The inferred cosmological parameters are consistent within 2$\sigma$ (or better) with those from better-established cosmological probes. This contrasts with our earlier findings using a larger, heterogeneous sample of 118 H$\beta$ AGNs, which yielded cosmological constraints differing by $\gtrsim 2\sigma$ from better-established cosmological probes. Our analysis demonstrates that sample homogeneity$-$specifically, the use of a consistent time-lag determination method$-$is crucial for developing RM AGNs as a cosmological probe.

In this paper, we introduce a scanner package enhanced by deep learning (DL) techniques. The proposed package addresses two significant challenges associated with previously developed DL-based methods: slow convergence in high-dimensional scans and the limited generalization of the DL network when mapping random points to the target space. To tackle the first issue, we utilize a similarity learning network that maps sampled points into a representation space. In this space, in-target points are grouped together while out-target points are effectively pushed apart. This approach enhances the scan convergence by refining the representation of sampled points. The second challenge is mitigated by integrating a dynamic sampling strategy. Specifically, we employ a VEGAS mapping to adaptively suggest new points for the DL network while also improving the mapping when more points are collected. Our proposed framework demonstrates substantial gains in both performance and efficiency compared to other scanning methods.

We use Matsuki's decomposition for symmetric pairs $(G, H)$ of (not necessarily compact) reductive Lie groups to construct the radial parts for invariant differential operators acting on matrix-spherical functions. As an application, we employ this machinery to formulate an alternative, mathematically rigorous approach to obtaining radial parts of Casimir operators that appear in the theory of conformal blocks, which avoids poorly defined analytical continuations from the compact quotient cases. To exemplify how this works, after reviewing the presentation of conformal 4-point correlation functions via matrix-spherical functions for the corresponding symmetric pair, we for the first time provide a complete analysis of the Casimir radial part decomposition in the case of Lorentzian signature. As another example, we revisit the Casimir reduction in the case of conformal blocks for two scalar defects of equal dimension. We argue that Matsuki's decomposition thus provides a proper mathematical framework for analysing the correspondence between Casimir equations and the Calogero-Sutherland-type models, first discovered by one of the authors and Schomerus.

Different variants of partial orders among quantum states arise naturally in the context of various quantum resources. For example, in discrete variable quantum computation, stabilizer operations naturally produce an order between input and output states; in technical terms this order is vector majorization of discrete Wigner functions in discrete phase space. The order results in inequalities for magic monotones. In the continuous variable case, a natural counterpart would be continuous majorization of Wigner functions in quantum phase space. Indeed, this concept was recently proposed and explored (mostly restricting to the single-mode case) in Van Herstraeten, Jabbour, Cerf, Quantum 7, 1021 (2023). In this work, we develop the theory of continuous majorization in the general $N$-mode case. In particular, we propose extensions to include states with finite Wigner negativity. Among our results, we prove a conjecture made by Van Herstraeten, Jabbour and Cerf for the convex hull of $N$-mode Gaussian states, and a phase space counterpart of Uhlmann's theorem of majorization.

We use a worldline-instanton formalism to study the momentum spectrum of Schwinger pair production in spacetime fields with multiple stationary points. We show that the interference structure changes fundamentally when going from purely time-dependent to space-time-dependent fields. For example, it was known that two time-dependent pulses give interference if they are anti-parallel, i.e. $E_z(t)-E_z(t-\Delta t)$, but here we show that two spacetime pulses will typically give interference if they instead are parallel, i.e. $E_z(t,z)+E_z(t-\Delta t,z-\Delta z)$. We take into account the fact that the momenta of the electron, $p_z$, and of the positron, $p'_z$, are independent for $E_z(t,z)$ (it would be $p_z+p'_z=0$ for $E(t)$), and find a type of fields which give moir\'e patterns in the $p_z-p'_z$ plane. Depending on the separation of two pulses, we also find an Aharonov-Bohm phase. We also study complex momentum saddle points in order to obtain the integrated probability from the spectrum. Finally, we calculate an asymptotic expansion for the eigenvalues of the Sturm-Liouville equation that corresponds to the saddle-point approximation of the worldline path integral, use that expansion to compute the product of eigenvalues, and compare with the result obtained with the Gelfand-Yaglom method.

We report on work using a newly developed code, SpheriCo.jl, that computes the gravitational collapse of a spherical scalar field, where the scalar can be either a classical field, or a quantum field operator. By utilising summation-by-parts methods for the numerical derivatives we are able to simulate the collapse longer than was possible previously due to enhanced numerical stability. We present a suite of tests for the code that tests its accuracy and stability, both for the classical and quantum fields. We are able to observe critical behavior of gravitational collapse for the classical setup, in agreement with expected results. The code is also used to compute two-point correlation functions, with results that hint at a non-trivial correlation across the horizon of Hawking quanta.

We consider nonlinear trident, $e^{\scriptscriptstyle -}\to e^{\scriptscriptstyle -} e^{\scriptscriptstyle -} e^{\scriptscriptstyle +}$, in various electric background fields. This process has so far been studied for plane-wave backgrounds, using Volkov solutions. Here we first use WKB for trident in time-dependent electric fields, and then for fields which vary slowly in space. Then we show how to use worldline instantons for more general fields which depend on both time and space.

Recent developments in the consistent embedding of general 4D static and spherically-symmetric spacetimes in arbitrary single-brane braneworld models [Phys.Rev.D 109 (2024) 4, L041501] initiated the program of studying the bulk structure of braneworld wormholes. In this article, adopting a completely generic approach, we derive the general conditions that the metric functions of any braneworld spacetime must satisfy to describe a wormhole structure in the bulk. Particular emphasis is placed on clarifying the proper uplift of 4D wormholes, expressed in terms of various radial coordinates on the brane, and we demonstrate the important role of the circumferential radius metric function for the embedding. Additionally, the flare-out conditions for braneworld wormholes are presented for the first time and are found to differ from the case of flat extra dimensions. To illustrate the method, we first perform the uplift into the Randall-Sundrum II braneworld model for three well-known 4D wormhole spacetimes; the effective braneworld wormhole solutions of Casadio-Fabbri-Mazzacurati and Bronnikov-Kim, and the Simpson-Visser spacetime. Subsequently, we study their bulk features by means of curvature invariants, flare-out conditions, energy conditions and embedding diagrams. Our analysis reveals that the assumption of a warped extra dimension has non-trivial implications for the structure of 5D wormholes.

We generalize Krylov construction to periodically driven (Floquet) quantum systems using the theory of orthogonal polynomials on the unit circle. Compared to other approaches, our method works faster and maps any quantum dynamics to a one-dimensional tight-binding Krylov chain. We also suggest a classification of chaotic and integrable Floquet systems based on the asymptotic behavior of Krylov chain hopping parameters (Verblunsky coefficients). We illustrate this classification with random matrix ensembles, kicked top, and kicked Ising chain.