Papers

From cosmology to quantum matter, metastable states often decay through the nucleation and growth of competing domains, with false vacuum decay providing the paradigmatic example of this process. Here we demonstrate a distinct regime in which domain growth outpaces nucleation by orders of magnitude and is controlled by local resonance conditions. Using a programmable quantum annealer with more than 4000 qubits, we realize a two-dimensional quantum Ising model whose metastable spin-polarized state encodes a false vacuum. At a specific value of the longitudinal field, single-spin flips at the boundary of a seeded bubble become resonant, enabling kinetically constrained expansion. Combining experiment with tensor-network simulations and stochastic circuit modeling, we observe nearly ballistic growth of true-vacuum domains with sub-ballistic interface broadening, consistent with Kardar–Parisi–Zhang universality. Our results establish a growth-dominated regime of false vacuum decay and show how large-scale quantum simulation can access nonequilibrium metastable dynamics relevant to quantum field theory, cosmology, and strongly correlated matter.

We study tree-level Yang–Mills wavefunctions in four-dimensional de Sitter space using their discontinuities. Cosmological cuts factorize gluon discontinuities into lower-point wavefunctions glued by cut propagators and transverse projectors. For ray-like trees and one-loop $n$-gons, the maximal cuts take a particularly simple form: a scalar $\phi^3$ discontinuity dressed by an ordered Yang–Mills numerator built from local gluing maps. We then use these cuts as reconstruction data for the four-, five-, and six-gluon wavefunctions in momentum space. The result separates into a cut-detectable part obtained from lower-point gluing and a cut-invisible completion fixed by current conservation and the flat-space limit. Through six points, the terms without longitudinal propagators follow the pole structure of color-ordered scalar $\phi^3+\phi^4$ wavefunctions, dressed by local Yang–Mills numerators. Longitudinal propagators collapse part of this scalar structure into contact-type contributions, with the first internal-line corrections appearing at six points. The reconstructed expressions agree with direct momentum-space Feynman-rule computations and give concrete low-point data for an all-$n$ organization of spinning de Sitter wavefunctions.

A codimension-one Carrollian CFT on null infinity has been proposed as the putative dual description of asymptotically flat spacetimes and has so far been successful in describing the massless S-matrices in one higher dimension. In this work, we investigate the current proposal of Carrollian holography to include the massive fields in the bulk. We discover a broader class of correlation functions in two-dimensional Carrollian CFTs and show that they encode massive scattering amplitudes in three-dimensional Minkowski spacetime. We also construct a bulk-to-boundary propagator that generalizes the one already existing for massless fields.

We establish a Wilson-line formulation of quark Reggeization in QCD. An interpolating operator for the Reggeized quark is identified in terms of semi-infinite Wilson lines, and its nonlinear rapidity evolution is derived. We provide strong evidence that this operator remains an eigenstate of the rapidity evolution up to next-to-leading logarithmic accuracy. Within the leading logarithmic accuracy, we explicitly recover the one-loop quark Regge trajectory. Our results provide a first-principles operator framework for quark Reggeization and pave the way for a systematic all-order description of high-energy QCD amplitudes with $t$-channel quark exchange in terms of Wilson lines.

Conventional quantum integrability is encoded in a commuting algebra of transfer matrices. By contrast, several models possess additional non-commuting conserved charges with important physical consequences, yet the nature of the corresponding symmetry has remained elusive. Focusing on the XXZ spin chain at roots of unity, we show that the non-Abelian analogue of the commuting transfer-matrix algebra is governed by quadratic relations following from a new class of unbalanced Yang–Baxter/RLL relations. This quadratic algebra is shown to encode precisely the Onsager algebra, for which we construct explicit matrix-product representations of both its generators and its duality defect line. The latter obeys $\mathbb{Z}_N$ Tambara–Yamagami fusion rules, thereby providing a lattice realization of the topological defect lines of the compactified boson conformal field theory. Our results identify non-Abelian transfer-matrix algebras as a microscopic origin for Onsager symmetry and dualities in lattice models.

By using the gauge-gravity duality, we study the holographic fermionic correlation functions in strongly coupled anisotropic plasmas. Starting from the isotropic AdS-Schwarzschild black brane background, we revisit the prescription for computing the retarded Green's function of a probe Dirac fermion and then generalize the formulas with respect to the anisotropic geometries. The method is applied to three distinct holographic models that capture different physical origins of anisotropy: axion-induced, magnetic-field-induced and unquenched-flavor-induced. Numerical results for the holographic correlation functions reveal direction-dependent corrections, negative dips in the imaginary part, Landau levels in the fermionic dispersion (magnetic field), and a momentum-independent pseudogap indicating an incoherent metallic phase (flavors). Our results complement and go beyond the hard thermal loop approximation, providing non-perturbative insights into fermionic excitations in strongly coupled anisotropic plasmas relevant for heavy-ion collisions and certain condensed matter systems.

We construct a discrete realization of two-dimensional Carroll dilaton gravity based on a BF-type gauge structure with holonomy variables on lattice links. The bulk theory remains topological, while the physical dynamics is encoded in boundary degrees of freedom. Imposing admissible boundary conditions, we derive the asymptotic symmetry structure directly at the lattice level. The least restrictive conditions yield an affine extension of the Carroll algebra, while additional constraints reduce the symmetry to a conformal sector governed by a discrete Virasoro-type algebra. In the continuum limit, the lattice symmetry structure reproduces the expected affine Carroll algebra together with its conformal reduction. The construction therefore provides the ultra-relativistic counterpart of discrete Jackiw-Teitelboim(JT) gravity.

We propose a relativistic quantum battery model consisting of an accelerated Unruh-DeWitt detector coupled to a massless scalar field in a de Sitter and anti-de Sitter spacetimes. The maximal amount of quantum extractable work, defined as the ergotropy, is used to probe Unruh-Hawking thermality induced by acceleration and spacetime curvature. Using the open quantum system approach, we study the dynamics of the ergotropy with respect to the Kubo-Martin-Schwinger temperature, spacetime boundary conditions, and dimensionality. It has been found that the asymptotic value of quantum work extraction is determined solely by the acceleration and curvature. The steady behavior in the two spacetimes can be unified to witness the global thermality which is independent of boundary conditions and dimensionality. From a local perspective, we investigate how the ergotropy evolves through different pathways as the battery gradually reaches the same thermal equilibrium state characterized by a certain KMS temperature. In dS spacetime, the evolution at large acceleration exhibits pronounced oscillations and differs from the fast thermal relaxation observed at low acceleration. Varying the boundary condition in AdS spacetime can improve the energy storage of the moving battery. When the dimension of AdS spacetime is increased, vacuum fluctuations can modestly amplify the ergotropy in the initial stage and facilitate the rapid thermalization. From the perspective of energy transfer, the relativistic quantum battery helps explore the thermal vacuum in curved spacetimes.

Inspired by the string theory, the braneworld picture introduces extra dimensions beyond the four that may have observable non-trivial effects in short distance (strong field) gravity experiments. A case in point is the Randall-Sundrum braneworld picture that projects the $5d$ bulk Weyl tensor onto the $3d$ brane providing a stress tensor in the effective Einstein field equations on the brane. Dadhich, Maartens, Papadopoulos and Rezania (DMPR) derived an exact braneworld black hole solution of the brane vacuum field equations. The solution formally resembles that of Reissner-Nordström but is physically different from it since the "tidal charge" $\Upsilon$ in the solution is not the electric charge but an imprint from the fifth dimension allowing both signs in the power law modification $\pm \frac{\Upsilon ^{2}}{r^{2}}$ to the Schwarzschild metric $\left( \Upsilon = 0\right)$. The corresponding black holes are designated as DMPR$\pm$. We study here the effect of $\Upsilon$ on strong field lensing observables and compare in the eikonal limit the ring down quasinormal mode (QNM) frequencies of DMPR$-$ with those of DMPR$+$, the two variants of tidal charge modified Schwarzschild black hole ($\Upsilon = 0$). It turns out that the tidal charge can significantly modify the Schwarzschild lensing observables and QNM frequencies. In particular, we find that the Pretorius-Khurana critical exponent $\gamma$ of circular null orbits in the DMPR$-$ black hole has a lower value than that for the Schwarzschild black hole, which indicates a stronger Lyapunov instability suggesting that the accretion disks of DMPR$-$ black holes would appear brighter. The case of the SgrA* black hole is considered for a possible constraint on $\Upsilon$ from the EHT observation of its shadow size.

Could the closest stellar or substellar object to the Sun be not an ordinary star at parsec distance, but a hidden-brane companion at hundreds or thousands of astronomical units? We do not perform a new Solar-System dynamics analysis; instead we construct a phenomenological mass-distance map using an illustrative ephemeris tidal envelope calibrated to Planet-Nine-like constraints. A smooth dark matter halo cannot supply such an object: the local density contains only a sub-Pluto mass within 1000 AU. A nearby hidden-brane companion must therefore be a structured, gravitationally bound object rather than a typical halo draw. The illustrative envelope still allows Earth to sub-Saturn masses at 300-1000 AU, rising to Jovian mass near 2000 AU. In a simple QCD-scaled hidden sector with a confinement scale about ten times larger than ordinary QCD, the minimum hidden stellar mass overlaps the upper part of this window, providing a benchmark for a genuine hidden-sector star: bright in dark photons, electromagnetically dark to us, and visible only through gravity. We also derive an Earth-based source-strength proxy for brane-to-brane channels and show that, along the ephemeris envelope, it grows as the square of the companion distance: the largest received source scale comes from the most massive companion still allowed, not the nearest one. A probe sent to the companion's gravitational projection would reduce the ordinary source-receiver separation by two to three orders of magnitude relative to Earth-based operation. This is not a detection forecast; the excitation of KK modes, the compact-direction brane-to-brane transfer factor, and the detector response remain model-dependent.

We show that every local scalar effective field theory admits a new kind of duality to an infinite class of local scalar field theories with distinct Lagrangians. The duality map takes the form of a field-dependent diffeomorphism, and cannot be obtained via purely local field redefinitions, nevertheless the dual theory has an identical $S$-matrix. The subset of interactions that maintain second-order equations of motion is non-trivially mapped into themselves under this transformation. We show how to couple generic scalar field theories to gravity in a way that preserves the duality. Crucially, this requires working in the Einstein-Cartan formalism, with the vielbein and spin connection treated as independent variables. When coupling to massless gravity, the duality is interpreted as a local field redefinition in which the vielbein transforms while the spin connection is held fixed; consequently, a torsion-free configuration is generically mapped to a dual configuration with non-zero torsion. We specify the general family of first-order gravitational theories that map into themselves under the duality. In the weak gravitational field limit, these reduce to scalar theories kinetically mixed with the graviton, which themselves form a family closed under the duality.

We construct an explicit boundary-action realization of superoscillatory initial states (SIS) for inflation, in which quantum interference within a band-limited initial wavefunctional generates a spectrally localized Bogoliubov excitation with a rapidly winding phase. Starting from a quadratic boundary term on the initial time surface, we derive the Bogoliubov coefficients and the resulting primordial curvature spectrum, obtaining a localized oscillatory feature fixed by the superoscillatory parameters $(a,N)$ rather than imposed phenomenologically. We compute the projection of this feature onto CMB angular power spectra and show that transfer-function smearing strongly suppresses the oscillatory component; full CAMB calculations confirm the qualitative effect and show that a simple Gaussian approximation overestimates the peak signal by about a factor of three. Using Planck 2018 TT data, we obtain an indicative matched-filter bound $\lambda \lesssim 0.05$ for a representative feature centered near the first acoustic peak, $\Delta k/k_* = 0.05$ at $k_* = 1.45\times 10^{-2}\,\mathrm{Mpc}^{-1}$. We further derive correlated predictions for polarization and the bispectrum, identify structural constraints that distinguish SIS from generic excited-state models, and show that galaxy clustering provides a qualitatively more powerful probe because it preserves the full oscillatory structure that CMB projection suppresses. This framework provides a concrete and testable realization of how initial-state quantum interference can imprint itself on cosmological observables.

Ten years ago, in a paper \cite{60}, a brief historical survey of the research activity in the Sector “Supersymmetry” at the Bogoliubov Laboratory of Theoretical Physics (BLTP) for more than 50 years of its existence has been given. Here, in commemoration of the 70th jubilee of Joint Institute for Nuclear Research, we review some recent sound advancements in this area. Specifically, we consider the issues of constructing the superfield quantum effective actions in $6D, {\cal N}=(1,0)$ supersymmetry and off-shell unconstrained superfield formulations of ${\cal N}=2$ higher spins. In both cases, the harmonic superspace approach plays the decisive role.

We build a BCFW-like recursion for cosmological correlators using the orthogonal Grassmannian. The key step is a bridge deformation that leaves all the Grassmannian constraints intact. The recursion relations are purely algebraic and avoid any spectral or radial integrals that usually appear in curved space. We obtain the gluon 4-point correlator using this bridge, producing two factorization poles, a total energy singularity coming from the three point building block, and a shifted energy singularity that emerges only after adding the two channels using recursion. We then show that the helicity stripped four-gluon correlator has the canonical form of a rectangle, where its boundaries represent various poles. We also describe the geometry of the gluon correlator in the Pfaffians as the natural coordinates in the Grassmannian. Using multiple deformation bridges, we also obtain the graviton four point correlator and observe a double-copy like relation at the level of the four point function, away from the physical cuts for each channel. We also extended the BCFW bridge formalism to the supersymmetric Grassmannian.

Modular flavour symmetries provide a possible organizing principle for the Standard Model Yukawa sector, by replacing generic couplings with a potentially small number of modular forms controlled by a single complex modulus. We study the extreme limit of this idea: \acp{OPM}, in which each charged-fermion mass matrix is fixed by a single modular invariant contraction. We develop a systematic method to construct such models, showing that the \ac{OPM} requirement is already highly constraining at the level of possible fermion hierarchies. In a concrete realization, the charged-lepton and down-quark sectors are controlled by the common modulus, leading to exact mass relations at the flavour scale, \[ m_s^5 = 2\sqrt{2}\,m_d^3m_b^2, \qquad m_\mu^3 = \sqrt{2}\,m_e m_\tau^2, \qquad m_s^2m_\tau = \sqrt{2}\,m_e m_b^2. \] We show that, once renormalization-group evolution and selective supersymmetric threshold effects are included, these high-scale relations can be made compatible with low-energy charged-fermion data. Our results provide a working proof of principle for \acp{OPM} and point towards a possible route to the flavour puzzle through highly

We derive an obstruction to Friedmann–Lemaître–Robertson–Walker (FLRW) daughter cosmologies from static, asymptotically flat regular black holes. The trapped region of such a parent is Kantowski–Sachs rather than FLRW, so the daughter must be introduced as a separate matched region. For closed daughters, the angular Darmois condition is controlled by the Misner–Sharp mass: asymptotic flatness and finite ADM mass force the induced density to decay as $A^{-3}$, while the $k=+1$ curvature term scales as $A^{-2}$. The minimal closed branch is therefore bounded rather than indefinitely expanding. Flat and open daughters avoid this boundedness mechanism. For their maximal homogeneous FLRW continuations, the regular-end affine-ANEC theorem excludes simultaneous non-staticity, curvature regularity, null geodesic completeness, and ANEC consistency. For Bardeen, the parent source does not naturally supply the late-time support needed for an unbounded closed daughter. Within these criteria, a viable FLRW daughter therefore requires additional structure, such as modified asymptotics, nonminimal matching, non-FLRW evolution, or an additional stress-energy component.

We explicitly show how moduli stabilization is realized geometrically in M-theory compactified on $T^4/\mathbb{Z}_2\, \times\, $K3, by using the Gibbons-Hawking approximation of the K3 metric. By relating this compactification to certain microstate geometries, we present the explicit solutions in which fully backreacted fluxes on certain four-cycles stabilize three of the $T^4/\mathbb{Z}_2$ compactification moduli. The minimal tadpole contribution of these fluxes is linear in the number of stabilized moduli, and we argue that this linear relation holds for more general fluxes. We also construct a one-parameter family of supersymmetric eleven-dimensional solutions that break Lorentz invariance and the warped-product structure of the compactification. These solutions are a continuous deformation of the warped-product Lorentz-invariant compactification, to which they reduce when the moduli reach their stabilized values. Away from the Lorentz-invariant locus, the fluxes are no longer self-dual in the internal space, and include fields that do not exist in the corresponding EFT. Remarkably, although these fluxes still stabilize a modulus, it is not the $T^4/\mathbb{Z}_2$ modulus that appears stabilized in the Lorentz-invariant solution, but rather a nontrivial combination of the $T^4$ volume and K3 shape moduli. The existence of these solutions suggests that the EFT description of moduli stabilization can be misleading and does not reflect the moduli-stabilization dynamics of the full eleven-dimensional theory. Our results extend straightforwardly to Type IIB String Theory compactified on orientifolds of $T^2 \times K3$.

We study cosmological gravitational particle production (CGPP) of dark matter in two-field inflationary backgrounds with both flat and curved field-space geometries. As a concrete realization of broader multifield mechanisms, we adopt a Starobinsky+quadratic potential and construct benchmark scenarios that interpolate between the flat field-space limit and the sidetracked attractor on a hyperbolic field space, and we compute the production spectrum of a gravitationally coupled spectator scalar for both minimal ($\xi = 0$) and conformal ($\xi = 1/6$) coupling to the Ricci scalar. We show that negative field-space curvature can strongly enhance the post-inflationary oscillations of the Ricci scalar, leading to an enhancement of up to an order of magnitude in the CGPP number density relative to the flat field-space limit, particularly for minimal coupling. For the sidetracked attractor, this enhanced production competes with a reduced inflationary energy scale, leading to a nontrivial dependence of the relic abundance on model parameters. We derive the relic abundance as a function of spectator mass and reheating temperature, and identify the viable parameter space for each benchmark. The conformal case $\xi = 1/6$, whose scalar mode equation is structurally analogous to that of a massive Dirac fermion, is much less constrained by isocurvature and provides a minimal scenario for purely gravitational dark matter production in multifield inflation.

Is the Universe infinite in all directions? The only way to know is to look. A non-trivial cosmic topology would imprint subtle signatures on the cosmic microwave background (CMB) and on the three-dimensional distribution of matter, breaking statistical isotropy and, potentially, homogeneity at the largest scales. If the topology scale is small enough, these signatures would be observable. Over the past three decades, successive space missions, most notably WMAP and $\textit{Planck}$, have enabled sophisticated searches for these signatures, using methods ranging from looking for matched circle pairs to full Bayesian likelihood analysis based on topology-dependent covariance matrices. Although these searches have yielded no definitive evidence for non-trivial topology, current constraints exclude only some topologies, parameter ranges, and observer positions. Recent advances show that detectable signals may persist even when the topology scale exceeds the size of the visible Universe. Planned CMB experiments, including LiteBIRD and $\textit{Taurus}$, and high-precision galaxy and line intensity-mapping surveys, could expand the detectable parameter space by exploiting polarisation data, and by exploring topology-induced correlations at all accessible redshifts. Whether cosmic topology is observable remains uncertain, but current and future data offer an unprecedented opportunity to probe the global structure of the Universe.

Recently, new positivity constraints were suggested to constrain arbitrary unitary tensor integrals. In the present work, we explore two variants of these positivity constraints: one built from “open bubbles”, which are tensor-like objects found by removing a tensor from a bubble invariant, and the second built from “color matrices”, which are matrices found by removing a color contraction from a bubble invariant. Using these positivity constraints, we find sharp bounds on unitary tensor integrals at finite $N$, and probe deviations from Gaussian universality in this limit.

A UV complete quantum field theory of general relativity is believed to require a non-perturbative approach. Moreover, background independence of classical general relativity supplies a physical selection for suitable Hilbert space representations of the quantum geometry and matter fields. In this contribution we show that, contrary to common intuition, there exist rigorous, background independent Fock representations available for a non-perturbative canonical quantisation of geometry and suitable matter fields. This is interesting because the Fock Hilbert space is separable while the Hilbert space of other manifestly background independent and non-perturbative canonical quantisation programmes is not. Since non-separability is a source for quantisation ambiguities, such a Fock representation may help to arrive at a significantly more predictive theory. As a simple application we discuss the cosmological truncation and mechanisms for quantum bounces. To make this manuscript concise we focus on the simplest incarnation of this idea. More details and many extensions are supplied in a companion paper.

We revisit the convergence region of the quasinormal modes expansion of Schwarzschild retarded Green functions from a radial scattering viewpoint. The tortoise coordinate admits a natural reflection about a distinguished point, which maps the original Regge-Wheeler problem to a mirror radial problem with the same quasinormal mode spectrum. Although this reflection is not a spacetime symmetry and does not leave the potential invariant, it gives a simple image interpretation of the second lightcone distance that controls convergence. Equivalently, after folding the radial line at the reflection point, the direct and mirror contributions arise as diagonal and off-diagonal propagation channels of a two-component half-line problem. We also relate this structure to the AdS$_2$ Green function, where the same direct-plus-image lightcone structure arises from a genuine boundary-bouncing null geodesic. This provides a spectral interpretation of the convergence condition and clarifies the role of the reflection point in the Schwarzschild radial Green function.

The Chen-Teo geometry is a Riemannian, Ricci-flat ALF 4-manifold, containing an AF gravitational instanton that gives the first counterexample to the Euclidean black hole uniqueness conjecture. We investigate the problem of constructing an Einstein analogue with a non-zero cosmological constant $\lambda$. We show that the solution is either the Plebański-Demiański metric with $\lambda$, or it has an anti-self-dual Weyl tensor. We study the latter case in detail: we prove that for $\lambda<0$, there is a conformal infinity separating two asymptotically hyperbolic metrics; we show that one of them is globally conformal to an ALE scalar-flat Kähler metric; we construct gravitational instantons with different topologies; and we show that the geometry is a 4-pole solution in the Calderbank-Pedersen classification.

Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$, making it relevant for $K<2/5$. Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.

Hypertoric (or toric hyperkähler) varieties are a class of symplectic singularities and their resolutions, obtained as Hamiltonian reductions of a symplectic vector space acted on by a torus. In physics, they appear as Higgs (and Coulomb) branches of 3d $\mathcal{N}=4$ supersymmetric quantum field theories with abelian gauge group. In this work, we construct an $\hbar$-adic (in the sense of microlocalisation) sheaf of vertex operator superalgebras over a given smooth hypertoric variety. Its global sections give the $A$-twisted boundary of the corresponding 3d gauge theory. We use this to prove that the associated affine variety of this hypertoric vertex operator superalgebra recovers the singular hypertoric variety. This proves the 3d Higgs branch conjecture for a large class of boundary vertex operator superalgebras. In particular, these vertex operator superalgebras are quasi-lisse. This is in contrast to the (purely even) hypertoric vertex operator superalgebras (and their $\hbar$-adic localisations) constructed previously by Kuwabara as global sections of sheaves on families of universal Poisson deformations of the hypertoric varieties. These are generally not quasi-lisse. We show that the vertex operator superalgebras defined in this paper are (fermionic) simple-current extensions of those defined by Kuwabara, and investigate the consequences for symplectic duality and characters. We observe that the latter are upgraded from partial (or false) theta functions to quasimodular forms.

The effective Hamiltonian of quantum chromodynamics in the front form of Hamiltonian dynamics is calculated and renormalized. The renormalization group procedure for effective particles up to the second order in the coupling constant is used. Small gluon mass is used to regulate infrared singularities of the theory. The counterterms necessary to renormalize the theory are determined by computing matrix elements of the effective Hamiltonian. The effective Hamiltonians are well-defined symmetric forms on a dense subspace of the Fock space. The zero modes are cut off but, once ultraviolet renormalization is performed, no divergences are found in the color singlet subspace in the limit of the gluon mass approaching zero. A major result is that the interplay between self-energy terms and gluon exchange effective terms generates a term proportional to the quadratic SU(3) Casimir operator times the logarithm of the gluon mass. Therefore, the matrix elements are logarithmically divergent in the color nonsinglet subspace, but finite in the color singlet subspace, because the Casimir operator vanishes in the color singlet subspace. The effective Hamiltonians are suitable for nonperturbative numerical calculations using either classical or quantum computers.

The $\omega$-effect in entangled neutral-meson systems provides a sensitive probe of CPT violation induced by quantum-gravitational environments. In open quantum systems, interactions with inaccessible gravitational degrees of freedom can render the reduced meson dynamics non-unitary, causing the CPT operator to become ill-defined, even when the underlying microscopic Hamiltonian is CPT invariant. We present a microscopic derivation of the $\omega$-effect arising from a multimode squeezed gravitational environment generated by an axion cloud around a Kerr black hole. Using the Takagi decomposition of the associated complex symmetric squeezing kernel, the graviton field is expressed in terms of independent squeezed supermodes possessing anomalous correlators. These correlators provide a microscopic quantum counterpart of the stochastic fluctuations that appear in earlier D-particle foam descriptions of the $\omega$-effect, replacing phenomenological variances of flavour-changing D-particle recoil by calculable graviton correlation functions. After tracing over the graviton bath, the anomalous correlators and the weak-interactions-induced mixing combine to generate transitions between the antisymmetric and symmetric two-meson sectors. This results in a small exchange-symmetric admixture, parametrised by $\omega$, in the otherwise antisymmetric EPR state. We obtain an explicit expression for $\omega$ in terms of a sum over Takagi supermodes weighted by their squeezing amplitudes and phases together with the weak-interaction flavour-mixing matrix element. The resulting framework suggests that the $\omega$-effect may be a generic signature of non-classical states of gravitational environments, extending beyond the specific axion-cloud scenario considered here. The observability of the $\omega$-effect from other astrophysical and microscopic black-hole sources is discussed.

The type IIB matrix model is expected to give a nonperturbative formulation of superstring theory. Its covariant derivative interpretation provides a method to describe curved spacetimes in the model. There, matrices are identified with certain covariant derivatives which can be viewed as infinite-size matrices. Here, by using the Berezin-Toeplitz quantization, we develop a method to regularize these matrices as finite-size ones, which is needed to calculate quantum effects in the interpretation or in particular to apply the interpretation to the results of numerical simulations. As examples, we examine the cases of $T^{2n}$ and $S^2$ in detail.

Euler regularized the divergent product of all natural numbers and found beautiful formulas for regularized sums of integer powers of natural numbers. These derivations essentially relied on what is now called the zeta-regularization technique, although analytical continuation had not yet been invented. This classic method is however not applicable to the product of all primes, as the prime zeta function has a natural boundary along the imaginary axis. Muñoz García and Pérez-Marco overcame this obstacle and evaluated the product of all primes to $4\pi^2$ by finding an appropriately regularized value of the derivative of the prime zeta function at the origin, lying on the natural boundary. We extend their approach in two novel directions. First, we show how to make sense of the sum of all primes. This regularization requires going a finite distance beyond the natural boundary. Second, we determine the regularized products of integers and primes in the nine imaginary quadratic fields where integers have a unique factorization into primes, and establish a general power-law relationship between products of integers and primes. Two well-known examples are Gauss and Eisenstein integers. The interest in this approach goes beyond number theory. In a variety of physical situations, the zeta-regularization technique is indeed not applicable because the relevant zeta function has a natural boundary.

"Colored" knot polynomials satisfy difference equation w.r.t. the highest weights of the underlying representation – which in the case of symmetrically colored Jones are named "quantum $A$-polynomials". In the double scaling quasiclassical (Kashaev) limit, when representation size $r\sim \hbar^{-1}$, there are different phases – in one of them the classical action vanishes and in another one it is a deformation of hyperbolic volume (of a knot complement in $S^3$). This corresponds to a splitting of the non-homogeneous version of the quantum $A$-polynomial into two pieces, which we illustrate by more examples than just a figure-eight knot $4_1$ in the original paper. From the point of view of quasiclassics, hyperbolic volume is just an integration constant, which is not fully determined by the $A$-polynomial equation – and actually remains ambiguous in this formalism. As a byproduct, we expect that classical $A$-polynomial at $L=1$ becomes proportional to Alexander: $A^{\cal K}(1,M)\sim \Delta^{\cal K}(M)$ – this seems true, but $A$ should be consistent with the polynomiality of non-homogeneous quantum ${\cal A}$-polynomial, what sometime implies that it is not minimal.