Algebraic non-covariant gauges are used often in string theory, Chern-Simons theory, gravitation and gauge theories. Loop integrals, however, have spurious singularities that need to be regularized. The most popular and consistent regularization is the Mandelstam- Leibbrandt(ML) prescription. This paper extends the ML prescription outside the light cone. It shares all the properties of light-cone ML regularization: It preserves naive power counting and gauge invariance. Moreover, using dimensional regularization(DR), we get a closed form for the basic integrals, including divergent and finite pieces. These results simplify calculations in gauge theories and open new avenues for applications in non-local models.

We revisit thermodynamics of five-dimensional AdS spacetime at finite temperature and rotation using the Euclidean path integral. It is generally believed that at low temperatures and finite rotation, the bulk saddle point that governs the thermodynamics describes a rotating gas of thermal radiation. Consequently, the dual gauge theory at low temperatures is in a confined thermal state. We demonstrate that this holographic expectation is at odds with the fact that, even at low temperatures, there exist saddles of the bulk path integral with real part of on-shell action smaller than that of the thermal rotating gas. The usual Kerr-AdS black holes but with complex parameters are examples of such saddles. Using mini-superspace ideas and steepest descent, we argue that these additional saddles do not actually feature in the low temperature partition function. This saves the original claim that rotating thermal gas is indeed the correct background for understanding the dual gauge theory at low temperatures. As a corollary, we also find that the unstable small rotating black hole does not contribute to the partition function at any temperature, even in a suppressed manner.

Few vacua are known for the three tachyon-free non-supersymmetric string theories. We find new classes of AdS backgrounds by focusing on spaces where the equations of motion reduce to purely algebraic conditions. Our first examples involve non-zero three-form fluxes supported either on direct product internal spaces or on $T_{p,q}$ geometries. For the ${\mathrm{SO}}(16)\times{\mathrm{SO}}(16)$ heterotic string, we then develop a method to engineer vacua with the addition of gauge fields. A formal Kaluza--Klein reduction yields complete solutions on a broad class of coset spaces $G/H$, automatically satisfying the three-form Bianchi identities with $H$-valued gauge fields.

Euclidean path integrals can be used to prepare states of a Lorentzian QFT. So long as any sources are turned off on the $t=0$ surface, the resulting Lorentzian states all belong to the same Hilbert space. Constructing more states than allowed by the Lorentzian density of states means that the resulting states must be linearly dependent. For large amplitude sources and a fixed cutoff on energy, the AdS bulk dual of this effect has been conjectured to be captured by spacetime wormholes. Wormholes should then be generic in the presence of large such Euclidean sources. This hypothesis can be studied in a context with asymptotically locally AdS$_4$ boundaries of topology $S^1 \times S^2$ in which the wormhole is supported by a source for minimally-coupled massless bulk scalars. In preparation for a later more complete study, we consider here a preliminary toy version of the model in which the spacetimes are cohomogeneity-1, but with the consequence that the sources do not vanish at $t=0$. We then find that generic sources at large masses do {\it not} lead to wormholes. Along the way we map out the phase diagram for wormhole, thermal AdS, and black hole phases of our cohomogeneity-1 ansatz. We also numerically evaluate their stability by identifying negative modes. In parallel with the previously-studied case of $S^3$ boundaries, the results are analogous to those associated with the familiar Hawking-Page transition.

We apply the quantum-mechanics bootstrap to supersymmetric quantum mechanics (SUSY QM) and to its matrix relative, the Marinari-Parisi model, which is conjectured to describe the worldvolume of unstable $D0$ branes. Using positivity of moment matrices together with Heisenberg, gauge, and (zero-temperature) thermal constraints, we obtain rigorous bounds on ground-state data. In the cases where SUSY is spontaneously broken, we find bounds that apply to the lowest-energy normalizable eigenstate. For $N = 1$ SUSY QM with a cubic superpotential, we obtain tight bounds that agree well with available approximation methods. At weak coupling they match well with the semiclassical instanton contribution to SUSY-breaking ground-state energy, while at strong coupling they exhibit the expected scaling and match well with Hamiltonian truncation. For the SUSY matrix QM, we construct a $44 \times 44$ bootstrap matrix and obtain bounds at large $N$. At strong coupling, we obtain the expected $E \sim \kappa \ g^{2/3}$ scaling of $E$ with $g$ and extract a lower bound on the coefficient $\kappa > .196$. At small coupling, the theory has a critical point $g_c$ where the two wells merge into one. We find a spurious kink at $g = \sqrt{2} g_c$. We attribute this to truncation error and solver limitations, and discuss possible improvements.

We explore the three-point amplitude of curvature perturbations in scenarios suggested by high-scale supersymmetry breaking in String Theory, where the inflaton is forced to climb a steep exponential potential. We can do it at the price of some simplifications, and more importantly with some assumptions on the softening effects of String Theory. These suggest a scenario proposed long ago by Gasperini and Veneziano, where the initial singularity is replaced by a bounce, and the resulting analysis rests on a scale $\Delta$ that leaves some signs in the angular power spectrum of the CMB. The amplitude comprises two types of contribution: the first oscillates around the original result of Maldacena and gives no further prospects to detect a non-Gaussian signal, but the second, which is subtly tied to the turning point at the end of the climbing phase, within the window 62<N<66 for the inflationary e-folds could be compatible with Planck constraints and potentially observable. The amplitudes involving the tensor modes contain only the first type of contribution.

Scalar fields in theories of gravity often inhabit a moduli space of vacua, and coherent spatial or temporal variations in their expectation values can produce measurable gravitational effects. Such variations are expected in contexts ranging from inflationary cosmology to the near-horizon regions of near-extremal black holes, where they can deflect light rays and shift horizons. This work derives a quantitative field excursion bound (FEB) on scalar variations along null geodesics, expressed in terms of the expansion parameter. The bound follows from the Raychaudhuri equation, assuming that all other fields satisfy the null energy condition (NEC). It is saturated in certain spacetimes containing a timelike naked singularity. A possible generalization to semiclassical spacetimes that violate the NEC, but satisfy a strengthened version of the quantum focusing condition (QFC), is proposed. In cosmology, the FEB constrains the extent of large field excursions to be linearly bounded by the number of e-folds, independent of the inflationary model. This has notable implications for anthropic scenarios, where large excursions are often invoked to access favorable vacua.

While the supergravity limit of AdS/CFT has been extensively explored, the regime in which stringy dynamics dominate, characterized by the emergence of an infinite tower of higher-spin massive modes, is far less understood. In this work, we leverage techniques from algebraic quantum field theory to investigate the extent to which hallmark features of bulk gravity survive at finite string tension and the emergence of intrinsically stringy phenomena. Working in the $g_s\rightarrow 0$ limit, we model excited string modes as free particles and demonstrate that the resulting Hagedorn spectrum leads to the breakdown of the split property, a strengthening of the locality principle, for regions that are within a string length of each other. We propose that this leads to a precise algebraic definition of stretched horizons and stretched quantum extremal surfaces. When stretched horizons exist, there is an associated nontrivial horizon $\star$-this http URL, applying the algebraic ER=EPR proposal leads to the emergence of type III${}_{0}$ von Neumann factors, which provide an intriguing characterization of how such regions can have a quantum Einstein-Rosen bridge even if they are geometrically disjoint.

We apply the universal method developed in \cite{Jiang:2025jnk} to compute the entanglement entropy between two tangent balls in CFT$_D$. When taking the radius of one ball to infinity, it gives the entanglement entropy between a ball and its tangent half plane. In two-dimensional case, this configuration is equivalent to the entanglement in boundary conformal field theory (BCFT) between the negative half-axis and an interval ending on the boundary.

We construct dimer graph for relativistic Toda chain associated with classical untwisted Lie algebra of A, B, C$_0$, C$_\pi$, D types and twisted A, D types. We show that the Seiberg-Witten curve of 5d $\CalN=1$ pure supersymmetric gauge theory of gauge group $G$ is a spectral curve of the relativistic Toda chain of the dual group $G^\vee$.

We construct a holographic model for an s+p superconductor with axion-induced translation symmetry breaking within the framework of gauge/gravity duality, working in the probe limit. The equations of motion are solved numerically to investigate the influence of the parameter $k/T$ on the competition and coexistence between the s-wave and p-wave orders. We find that increasing $k/T$ suppresses the thermodynamic stability of both the single condensate s-wave and p-wave solutions. With the $k-\mu$ phase diagram and the condensate curves, we see that the region dominated by the single condensate p-wave phase gradually decreases with the increasing of $k/T$, finally leaving only the single condensate s-wave phase in the large $k/T$ region, which is explained by the grand potential curves showing a slower decreasing of the thermodynamic stability for the s-wave solution than that for the p-wave solution. Furthermore, a larger minimum ratio of the charges $q_p/q_s$ is required to stabilize the s+p coexistent phase as $k/T$ increases, and we determine the precise dependence of this critical ratio on $k/T$. Finally, our study of the optical conductivity reveals that the gap frequency increases with $k/T$. A characteristic kink, associated with the s+p coexistent phase, is identified in the dependence of gap frenquency on $k/T$, which could serve as a potential experimental signature for detecting multi-condensate superconductivity.

We study dissipative effects for a system consisting of a massless real scalar field satisfying Neumann boundary conditions on a space and time-dependent surface, in d+1 dimensions. We focus on the comparison of the results for this system with the ones corresponding to Dirichlet conditions, and the same surface space-time geometry. We show that, in d=1, the effects are equal up to second order for rather arbitrary surfaces, and up to fourth order for wavelike surfaces. For d>1, we find general expressions for their difference.

To each four dimensional $\mathcal{N}\geq 2$ supersymmetric quantum field theory, one can associate an algebraic completely integrable (ACI) system that encodes the low energy dynamics of theory. In this paper we explicitly derive the appropriate ACI systems for the global forms of $\mathcal{N}=4$ super Yang-Mills (sYM) using isogenies of polarised abelian varieties. In doing so, we relate the complex moduli of the resulting varieties to the exactly marginal coupling of the theory, thus allowing us to probe the $S$-duality groups of the global forms. Finally, we comment on whether the resulting varieties are the Jacobians of a minimal genus Riemann surface, coming to the conclusion that many global forms of $\mathcal{N}=4$ sYM do not admit a minimal genus Seiberg-Witten curve that correctly reproduces the global form.

The low energy effective theory on the moduli space of vacua of 4d superYang-Mills (sYM) theory defines a special Kähler geometry. For simple sYM gauge algebras, $\mathfrak{g}$, we classify all compatible special Kähler structures by showing that they are in one-to-one correspondence with certain equivalence classes of integral symplectic representations of the Weyl group of $\mathfrak{g}$. We further demonstrate that, for principal Dirac pairing, these equivalence classes are in one-to-one correspondence with the S-duality orbits of the global structures of the corresponding $\mathfrak{g}$ sYM gauge theory, after a mistake in the field theory literature is corrected. This provides a low-energy test of S-duality. We also discuss twisted product geometries made from factors with special Kähler structures with non-principal Dirac pairings.

We investigate the solution-generating technique based on the Breitenlohner-Maison (BM) linear system, for asymptotically flat, stationary, bi-axisymmetric black hole solutions with various horizon topologies in five-dimensional vacuum Einstein theory. We construct the monodromy matrix associated with the BM linear system, which provides a unified framework for describing three distinct asymptotically flat, vacuum black hole solutions with a single angular momentum in five dimensions, each with a different horizon topology: (i) the singly rotating Myers-Perry black hole, (ii) the Emparan-Reall black ring, and (iii) the Chen-Teo rotating black lens. Conversely, by solving the corresponding Riemann-Hilbert problem using the procedure developed by Katsimpouri et al., we demonstrate that factorization of the monodromy matrix exactly reproduces these vacuum solutions, thereby reconstructing the three geometries. These constitute the first explicit examples in which the factorization procedure has been carried out for black holes with non-spherical horizon topologies. In addition, we discuss how the asymptotic behavior of five-dimensional vacuum solutions at spatial infinity is reflected in the asymptotic structure of the monodromy matrix in the spectral parameter space.

We investigate a novel class of defects in the critical $\mathrm{O}(2N)$ model that preserve conformal symmetry along the defect, but not the symmetry under rotations transverse to the defect. Instead, they only preserve a combination of transverse rotations and a global symmetry. These defects are constructed as IR fixed points of RG flows originating at monodromy defects, triggered by a relevant operator with non-zero transverse spin. Using large-$N$ and $4-\varepsilon$ expansions, we compute leading-order scaling dimensions of defect operators and the one-point functions of the bulk fields. In various limits this theory coincides with the monodromy defect or the pinning field defect, and we compare our results to existing results for these defects.

In this work, we investigate the velocity effects on information degradation due to the Unruh effect in accelerated quantum systems (with finite interaction time). We consider a detector moving along a spatial trajectory within a two-dimensional plane. The quantum systems studied were: accelerated single-qubit, quantum interferometric circuit, and which-path distinguishability circuit. Thus, for non-relativistic velocity regime, we obtained analytical expressions such as transition rates, quantum coherence, visibility, distinguishability, and the complementarity relation. On the other hand, for the ultra-relativistic velocity regime, we saw that the Unruh effect is suppressed and therefore the detector does not respond in this case. Our findings revealed that velocity effects imply mitigation of information degradation, this interesting behaviors happen because of the composite effect of both velocity and acceleration. The results obtained show that the addition of the non-relativistic, transverse and constant motion of an accelerated detector can play a protective role in quantumness in systems at high accelerations, although the effects are very small.

We discuss the emission of pairs of photons by charges with generic worldlines in the Minkowski vacuum from the viewpoint of inertial observers and interpret them from the perspective of Rindler observers. We show that the emission of pairs of Minkowski photons corresponds, in general, to three distinct processes according to Rindler observers: scattering, and emission and absorption of pairs of Rindler photons. In the special case of uniformly accelerated charges, the radiation observed in the inertial frame can be fully described by the scattering channel in the Rindler frame. Therefore, the emission of pairs of Minkowski photons -- commonly referred to as Unruh radiation -- can be seen as further evidence supporting the Unruh effect.

We consider the background cosmological solutions in the $6D$ (six-dimensional) model with one time and five space coordinates. The theory of our interest has the action composed by the Einstein term, cosmological constant, and two conformal terms constructed from the third powers of the Weyl tensor. It is shown how the highest derivative terms in the equations of motion can be isolated that opens the way for their numerical integration. There are flat anisotropic solutions which make one of the flat isotropic subspaces to be static. Depending on the value of bare cosmological constant, either two-dimensional or three-dimensional subspace can be static. In particular, there is a physically favorable solution with three ``large'' space coordinates and two extra inner dimensions stabilized. This solution is stable for a wide range of coupling constants, but this requires a special value of the bare cosmological constant.

The Weyl double copy formalism, which relates the Weyl spinor with the square of the field strength, is studied in the context of Hassan-Rosen bigravity for stationary and time-dependent solutions. We consider the dyonic Kerr-Newman-(A)dS solution and the Plebański-Demiański metric in the context of bigravity. These solutions are studied in the Weyl double copy both with matter independently coupled and show that no massive modes are present in the Weyl spinor. The equations of motion for the gauge and scalar fields are those of Maxwell equations coupled to an external source, and massless Klein-Gordon equations with a conformal curvature term and an external source, all of them consistent with general relativity. For wave solutions, massive modes are manifest in the Weyl spinor and a formulation in bigravity for these massive modes is proposed. The resulting equations of motion are Proca equations with a conformal term and massive Klein-Gordon equations. In the case of the matter contributions for waves, we show how the resonance mass is present in equations of motion of the fields obtained from the Weyl double copy. The solutions studied are written in a Kerr-Schild form, connecting with the Kerr-Schild double copy.

Oscillons are long-lived nonlinear pseudo-solitonic configurations of scalar fields and many plausible inflationary scenarios predict an oscillon-dominated phase in the early universe. Many possible aspects of this phase remain unexplored, particularly oscillon-oscillon interactions and interactions between oscillons and their environment. However the primary long range forces between oscillons are gravitational and thus slow-acting relative to the intrinsic timescales of the oscillons themselves. Given that simulations with local gravity are computationally expensive we explore these effects by extracting individual specimens from simulations and then engineering interactions. We find that oscillons experience friction when moving in an inhomogeneous background and, because oscillons in non-relativistic collisions bounce or merge as a function of their relative phases, the outcomes of interactions between ``wild'' oscillons depend on their specific trajectories.

The unsuppressed CP violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle $\bar \theta$ indicates the CP invariance at the fundamental level. Thus, the small ${\bar \theta}$ is technically natural, since we have an enhanced CP symmetry in the limit of the vanishing $\bar \theta =0$. In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model which guarantees the real determinants of the quark mass matrices assuming a non-invertible symmetry.

Non-local gravity can potentially solve several problems of gravitational field both at Ultra-Violet and Infra-Red scales. However, such an approach has been formulated mainly in metric formalism. In this paper, we discuss non-local theories of gravity in the metric-affine framework. In particular, we study the dynamics of metric-affine analogue of some well-studied non-local theories, by treating the metric and the connection as independent fields. The approach gives the opportunity to deal with non-local gravity under a more general standard. Furthermore, we introduce some novel non-local metric-affine theories with no Riemannian analogue and investigate their dynamics. Finally we discuss some cosmological applications of our development.

In this paper, we utilize the maximum entropy prescription to determine a quantum state of a small collision system at the kinetic freeze-out. We derive expressions for multiplicity-selected particle momentum spectra and correlation functions by applying a fixed particle number constraint to this state. The results of our analysis may be useful for interpreting the multiplicity dependence of the particle momentum spectra and correlations in high-multiplicity $pp$ collision events at a fixed LHC energy.

We discuss photon rings around as well as shadows of Kerr black holes immersed in a swirling spacetime. We find that the spin-spin interaction between the angular momentum of the black hole and the swirling of the background leads to new interesting effects as it breaks the symmetry between the upper and lower hemispheres. One of the new features of the spin-spin interaction is the existence of up to three light rings for suitable choices of the angular momentum parameter $a$ and swirling parameter $j$. In comparison to the Schwarzschild black hole immersed in a swirling universe, the light rings typically all possess different radii.

Simulating nonequilibrium dynamics of quantum many-body systems is one of the most promising applications of quantum computers. However, a faithful digital quantum simulation of the Hamiltonian evolution is very challenging in the present noisy quantum devices. Instead, nonequilibrium dynamics under the Floquet evolution realized by the Trotter decomposition of the Hamiltonian evolution with a large Trotter step size is considered to be a suitable problem for simulating in the present or near-term quantum devices. In this work, we propose simulating the many-body localization crossover as such a nonequilibrium problem in the disordered Floquet many-body systems. As a demonstration, we simulate the many-body localization crossover in a disordered kicked Ising model on a heavy-hex lattice using $60$ qubits from $156$ qubits available in the IBM Heron r2 superconducting qubit device named ibm\_fez. We compute out-of-time-ordered correlators as an indicator of the many-body localization crossover. From the late-time behavior of out-of-time-ordered correlators, we locate the quantum chaotic and many-body localized regimes as a function of the disorder strength. The validity of the results is confirmed by comparing two independent error mitigation methods, that is, the operator renormalization method and zero-noise extrapolation.

We show that the threshold to form a black hole, in an asymptotically flat and radiation dominated Friedman-Robertson-Walker (FRW) Universe, is not solely (mainly) determined by the behaviour of the compaction function at its maximum, as earlier thought, but also by the three-dimensional curvature at smaller (but super-horizon) scales, which we call "the core". We find three classes of initial conditions characterized by an open (O), closed (C), or flat (F) FRW core surrounded by a shell with higher three-dimensional curvature. In the C case, the core helps the collapse so that the black hole formation threshold is there the lowest among all cases. Type-II black holes might only be generated by Type-O or F (each of those with different thresholds, with O being the highest) or by a Type-C with an effective F core. Finally, we argue that an F core is typically more probable for a sharp power spectrum, however, it is also more likely related to non-spherical initial conditions. On the other hand, a very broad power spectrum, which might be related to the observed NanoGrav signal, would favor the formation of Type-I black holes with a mass spectrum peaked at the Infra-Red scale.

The universality of free fall is one of the most cherished principles in classical gravity. Its fate in the quantum world is one of the key questions in fundamental physics. We investigate the universality of free fall in the context of Planck scale modifications of Newtonian gravity. Starting from a doubly-special-relativity setting we take the Newtonian limit to obtain deformed Galilean relativity. We study the interaction between two test particles, subject to deformed Galilean relativity, and a classical, undeformed gravitational source, the Earth. Such an interaction is investigated here for the first time. Considering the two test particles falling freely in the source's gravitational field, we examine whether the universality of free fall is affected by deformed relativistic symmetries. We show that, in general, the universality of free fall is violated. Remarkably, we find that there exist distinguished models for which the universality of free fall is realized and which predict a specific modification of the Newtonian potential.

We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its value within MSSM. We combine a superpotential, which is uniquely determined by applying a continuous R symmetry, with two fractional shift-symmetric Kaehler potentials introducing two free parameters (p,N). The inflationary observables provide an excellent match to the recent ACT data for 1.355<=p<=6.7 and 6x10^-5<= N<=0.7. The attainment of inflation allows for subplanckian inflaton values and possibly detectable primordial gravitational waves with (p,N) values of order unity. A solution to the mu problem of MSSM and baryogenesis via non-thermal leptogenesis can be also accommodated extending the superpotential of the model with suitable terms.

The prediction of the anomalous gyromagnetic factor of the electron, started with the evaluation of the electromagnetic contribution by Schwinger (1948) and of the weak contribution by Jackiw and Weinberg (1972), is one of the major successes of Quantum Field Theory and the Standard Model. The results obtained truncating the series are in spectacular agreement with experiments. Yet, a mathematical justification and an estimate of the truncation error are problematic, being such series diverging and not asymptotic to any QFT. For a non perturbative result, one has to consider the Standard Model as an effective theory valid up to certain energy scales. In this paper we consider the neutral sector of the Electroweak model with a momentum cutoff; we rigorously prove that the anomalous gyromagnetic factor in the effective regularized theory coincides with the Jackiw-Weinberg result, obtained by the truncation of the formal expansion with no cutoffs (whose sum is not expected to exist), up to a regularization-dependent correction which is subdominant in the weak coupling regime if the cutoff is smaller than the inverse coupling and larger than the boson mass. The proof is based on a convergent expansions and Renormalization Group (RG) methods; cancellations based on exact and approximated symmetries are needed to get lowest order dominance.

BTZ spacetime is a long-known locally AdS solution to the Einstein equations in 1 timelike and 2 spacelike dimensions. Its static variant is interpreted as a black hole whose mass is related to the period of the angular coordinate. This solution can be parametrically continued into one without horizons but with a conical deficit in the center. Such a solution is interpreted as a spacetime with a massive particle. It has been shown that this particle can be in static equilibrium with a cosmic string passing through the spacetime to infinity. In this work, we explore the interaction of point particles with strings, such as a bound system of two particles connected by a string of finite length. We identify additive local mass in the static spacetimes and apply it to the case of particles and strings. Finally, using the cut and glue method, we construct the system of two particles oscillating on the string, which goes out of the scope of static systems.

The connection between simple Lie algebras and their Yangian algebras has a long history. In this work, we construct finite-dimensional representations of Yangian algebras $\mathsf{Y}(\mathfrak{sl}_{n})$ using the quiver approach. Starting from quivers associated to Dynkin diagrams of type A, we construct a family of quiver Yangians. We show that the quiver description of these algebras enables an effective construction of representations with a single non-zero Dynkin label. For these representations, we provide an explicit construction using the equivariant integration over the corresponding quiver moduli spaces. The resulting states admit a crystal description and can be identified with the Gelfand-Tsetlin bases for $\mathfrak{sl}_{n}$ algebras. Finally, we show that the resulting Yangians possess notable algebraic properties, and the algebras are isomorphic to their alternative description known as the second Drinfeld realization.

Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum geometries observed in lattice quantum gravity. We tested seven supervised and seven unsupervised machine learning models and found that most of them were very successful in that task, even outperforming standard methods based on order parameters.

Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can derive a quantum generalization of the Fisher information matrix in a natural way as the Hessian matrix arising in a Taylor expansion of a smooth divergence. Such an approach is appealing for quantum information theorists, given the ubiquity of divergences in quantum information theory. In contrast to the classical case, there is not a unique quantum generalization of the Fisher information matrix, similar to how there is not a unique quantum generalization of the relative entropy or the Rényi relative entropy. In this paper, I derive information matrices arising from the log-Euclidean, $\alpha$-$z$, and geometric Rényi relative entropies, with the main technical tool for doing so being the method of divided differences for calculating matrix derivatives. Interestingly, for all non-negative values of the Rényi parameter $\alpha$, the log-Euclidean Rényi relative entropy leads to the Kubo-Mori information matrix, and the geometric Rényi relative entropy leads to the right-logarithmic derivative Fisher information matrix. Thus, the resulting information matrices obey the data-processing inequality for all non-negative values of the Rényi parameter $\alpha$ even though the original quantities do not. Additionally, I derive and establish basic properties of $\alpha$-$z$ information matrices resulting from the $\alpha$-$z$ Rényi relative entropies. For parameterized thermal states, I establish formulas for their $\alpha$-$z$ information matrices and hybrid quantum-classical algorithms for estimating them, with applications in quantum Boltzmann machine learning.

String theories naturally predict a negative, while observations on the exponential expansion of the present Universe requires a positive value for the cosmological constant $\Lambda$. Solution to resolve this discrepancy is known in the framework of string theory and given for Asymptotically Safe (AS) quantum gravity by using Renormalization Group (RG). However, the former might describes unstable worlds and the latter lacks the inclusion of temperature which is otherwise crucial in the early Universe. Here we present a proposal for resolving this conflict by using a modified thermal RG method where the temperature parameter $T$ is given by the inverse radius of the compactified time-like dimension, similarly to spacetime foliation. In our scenario not the dimensionful temperature $T$, but the dimensionless temperature $\tau = T/k$ is kept constant when the RG scale $k$ is sent to zero and string theory is assumed to take place at very high while AS quantum gravity at intermediate and low temperatures. We show that the modified thermal RG study of AS quantum gravity models at very high temperatures results in a negative cosmological constant while turns it into a positive parameter for low temperatures.

Due to their iconic linearly vanishing density of states near the zero-energy, half-filled two-dimensional Dirac materials in flat Euclidean and negatively-curved hyperbolic spaces exhibit dynamic mass generation only once a critical interaction strength is surpassed. Application of external magnetic fields onto these systems can, however, trigger the formation of such ordered phases yielding isotropic insulation near the band-center at arbitrarily weak coupling, a phenomenon known as magnetic catalysis. Recently, it has been proposed that a specific type of non-Hermiticity, allowing the system to feature an all-real eigenvalue spectrum otherwise squeezed toward the zero-energy, can bring down the requisite critical coupling of a specific family of ordered phases, commuting class masses, to a desired lower finite value in Dirac systems, a phenomenon known as non-Hermitian catalysis (arXiv:2501.18591). Here, we predict that a confluence of external magnetic fields and such a non-Hermiticity can amplify the magnitude of commuting class masses for subcritical strengths of interactions in Dirac liquids, an emergent phenomenon named non-Hermitian amplification of magnetic catalysis. We anchor this prediction from numerical self-consistent mean-field solutions of the commuting class mass charge-density-wave (antiferromagnetic) order displaying a staggered pattern of average electronic density (magnetization) between the nearest neighboring sites of the half-filled Euclidean honeycomb and hyperbolic {10, 3} and {14, 3} lattices, all featuring emergent non-Hermitian Dirac quasiparticles, after decomposing the nearest-neighbor Coulomb (on-site Hubbard) repulsion in the Hartree channel. We discuss the scaling behavior of these two orders with magnetic field and non-Hermiticity over a wide range of subcritical interactions.. Possible experimental setups to test our predictions are discussed.

We investigate anomalies in the class of non-local field theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by string field theory and ghost-free non-local approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired non-local extension of QED. We show that the vector anomaly vanishes as required by gauge-invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in scale of non-locality. We also calculate the non-local vector and axial currents explicitly, and present an illustrative example by applying our results to the decay of \pi_0 \rightarrow \gamma\gamma.

We construct the M5-brane limit of eleven-dimensional supergravity. The resulting action is invariant under Galilean boosts and has a local scale symmetry. We also consider the limit of the equations of motion where we recover a Poisson-like equation arising from an M5-brane source but which does not follow from the non-relativistic action. We argue that the resulting theory describes gravitational fluctuations around a stack of M5-branes, represented by a trivial Minkowskian spacetime, but where the number of M5-branes is determined by the flux of a Lagrange multiplier field.

Three-dimensional supersymmetric Chern-Simons Matter (CSM) theories typically preserve $ \mathcal{N}=3$ supersymmetry but can exhibit enhanced $\mathcal{N}=4$ supersymmetry under special conditions. A detailed understanding of the moduli space of CSM theories, however, has remained elusive. This paper addresses this gap by systematically analysing the maximal branches of the moduli space of $\mathcal{N}=3$ and $\mathcal{N}=4$ CSM realised via Type IIB brane constructions. Firstly, for $\mathcal{N}=4$ theories with Chern-Simons levels equal $1$, the $\mathrm{SL}(2,\mathbb{Z})$ dualisation algorithm is employed to construct dual Lagrangian 3d $\mathcal{N}=4$ theories without CS terms. This allows the full moduli space to be determined using quiver algorithms that compute Higgs and Coulomb branch Hasse diagrams and associated RG flows. Secondly, for $\mathcal{N}=4$ theories with CS-levels greater $1$, where $\mathrm{SL}(2,\mathbb{Z})$ dualisation does not yield CS-free Lagrangians, a new prescription is introduced to derive two magnetic quivers, $\mathsf{MQ}_A $ and $\mathsf{MQ}_B$, whose Coulomb branches capture the maximal A and B branches of the original $\mathcal{N}=4$ CSM theory. Applying the decay and fission algorithm to $ \mathsf{MQ}_{A/B}$ then enables the systematic analysis of A/B branch RG flows and their geometric structures. Thirdly, for $\mathcal{N}=3$ CSM theories, one magnetic quiver for each maximal (hyper-Kähler) branch is derived from the brane system. This provides an efficient and comprehensive characterisation of these previously scarcely studied features.

Recent work has demonstrated that Euclidean Giddings-Strominger axion wormholes are stable in asymptotically flat 4D Minkowski spacetime, suggesting that they should, at least naively, be included as contributions in the quantum gravitational path integral. Such inclusion appears to lead to known wormhole paradoxes, such as the factorization problem. In this paper, we generalize these results to AdS3 spacetime, where the axion is equivalent to a U(1) gauge field. We explicitly construct the classical wormhole solutions, show their regularity and stability, and compute their actions for arbitrary ratios of the wormhole mouth radius to the AdS radius and across various topologies. Finally, We discuss potential implications of these findings for the 3D gravitational path integral.

We consider properties of the gravitational path integral, ${Z}_{\text{grav}}$, of a four-dimensional gravitational effective field theory with $\Lambda>0$ at the quantum level. To leading order, ${Z}_{\text{grav}}$ is dominated by a four-sphere saddle subject to small fluctuations. Beyond this, ${Z}_{\text{grav}}$ receives contributions from additional geometries that may include Einstein metrics of positive curvature. We discuss how a general positive curvature Einstein metric contributes to ${Z}_{\text{grav}}$ at one-loop level. Along the way, we discuss Einstein-Maxwell theory with $\Lambda>0$, and identify an interesting class of closed non-Einstein gravitational instantons. We provide a detailed study for the specific case of $\mathbb{C}P^2$ which is distinguished as the saddle with second largest volume and positive definite tensor eigenspectrum. We present exact one-loop results for scalar particles, Maxwell theory, and Einstein gravity about the Fubini-Study metric on $\mathbb{C}P^2$.

We propose and study a family of complex matrix models computing the protected two- and three-point correlation functions in $\mathcal{N}=4$ SYM. Our description allows us to directly relate the eigenvalue density of the matrix model for ``Huge" operators with $ \Delta \sim N^2$ to the shape of droplets in the dual Lin-Lunin-Maldacena (LLM) geometry. We demonstrate how to determine the eigenvalue distribution for various choices of operators such as those of exponential, character, or coherent state type, which then allows us to efficiently compute one-point functions of light chiral primaries in generic LLM backgrounds. In particular, we successfully match the results for light probes with the supergravity calculations of Skenderis and Taylor. We provide a large $N$ formalism for one-point functions of ``Giant" probes, such as operators dual to giant graviton branes in LLM backgrounds, and explicitly apply it for particular backgrounds. We also explicitly compute the correlator of three huge half-BPS operators of exponential type and stacks of determinant operators by reducing them to the known matrix model problems such as the Potts or $O(n)$ model on random planar graphs. Finally, we point out a curious relation between the correlators of $\frac{1}{4}$-BPS and $\frac{1}{8}$-BPS coherent state operators and the Eguchi-Kawai reduction of the Principal Chiral Model in $2D$ and $3D$ correspondingly.

The connected wedge theorem states that in order to have a scattering process in the bulk, it is necessary to have $O(1/G_N)$ mutual information between certain "decision" regions in the boundary theory. While this large mutual information is not generally sufficient to imply scattering, arXiv:2404.15400 showed that for a certain class of geometries, bulk scattering is implied by a certain relation between two (possibly non-minimal) Ryu-Takayanagi surfaces. Here, we show that the 2-to-2 version of the theorem becomes an equivalence in pure AdS$_3$: large mutual information between appropriate boundary subregions is both necessary and sufficient for bulk scattering. This result allows us to extend the findings of arXiv:2404.15400 to a broader class of asymptotically AdS$_3$ spacetimes, which we illustrate with the spinning conical defect geometry. In contrast, we find that matter sources can disrupt this converse relation, and that the $n$-to-$n$ version of the theorem with $n>2$ lacks a converse even in the AdS$_3$ vacuum.

We investigate symmetry topological field theories (SymTFTs) of non-abelian and non-invertible symmetries and the different Lagrangian algebras associated with a given Drinfeld center. For several examples we analyze the condensable algebras of the Drinfeld center to identify the intrinsically gapless symmetry protected topological (igSPT) phases. In previous work, the relation between igSPT phases and resolving anomalies by embedding an anomalous symmetry inside a larger fusion category was demonstrated. Here we present more examples of this mechanism that involve both group-like and categorical symmetries.

The Kerr-Schild double copy is celebrated for producing exact gravitational spacetimes from gauge fields, yet the preservation of symmetry content remains largely unexplored. We investigate the fate of residual symmetries in the Kerr-Schild double copy, focusing on the Schwarzschild solution. On the gauge theory side, we derive the residual transformations that preserve the Abelian and non-Abelian Kerr-Schild ansatzë, finding they both form an infinite-dimensional Lie algebra parameterized by arbitrary null functions. On the gravity side, we analyze the resulting residual diffeomorphisms of the Kerr-Schild Schwarzschild metric. Restricting our focus to the Killing vector class of solutions, we find that the only surviving diffeomorphisms are the finite-dimensional global isometries of Schwarzschild, reducing the residual gauge algebra to the Poincaré subalgebra containing exclusively time translations and spatial rotations. This finding confirms a fundamental structural mismatch: the infinite-dimensional algebra of the gauge side admits no analogous structure in this gravitational sector. We formalize this by showing that the BRST operator for the residual symmetry is trivialized under the Killing condition, establishing the consistency of this algebraic reduction within a quantum field theoretic framework. This paper is the first of a two-part series. In the second paper, we complete this analysis by examining the more complex proper conformal Killing vector class of solutions and formulating a unified BRST framework.

We complete our investigation into the residual symmetries of the Kerr-Schild double copy for the Schwarzschild solution. In the first paper in this series, we showed that the infinite-dimensional residual gauge algebra collapses to the finite-dimensional global isometries when restricted to Killing vectors. Here, we extend the analysis to proper conformal Killing vectors (CKVs), solving the field equations via the method of characteristics to obtain explicit conformal solutions. While asymptotic flatness and horizon regularity remove divergent contributions, the surviving components form a non-trivial infinite-dimensional algebra, revealing a structural mismatch with the canonical Schwarzschild solution. We resolve this by constructing a unified, Weyl-compensated BRST complex, showing that the infinite-dimensional modes are BRST-exact and do not correspond to physical degrees of freedom. This demonstrates the quantum consistency of the Kerr-Schild double copy, confirming that the physical spectrum is restricted to global isometries.

We study non-thermal resonant leptogenesis in a general setting where a heavy majoron $\phi$ decays to right-handed neutrinos (RHNs) whose further out-of-equilibrium decay generates the required lepton asymmetry. Domination of the energy budget of the Universe by the $\phi$ or the RHNs alters the evolution history of the primordial gravitational waves (PGW) of inflationary origin, which re-enter the horizon after inflation, modifying the spectral shape. The decays of $\phi$ and RHNs release entropy into the early Universe while nearly degenerate RHNs facilitate low and intermediate-scale leptogenesis. A characteristic damping of the GW spectrum resulting in knee-like features would provide evidence for low-scale non-thermal leptogenesis. We explore the parameter space for the lightest right-handed neutrino mass $M_1\in[10^2,10^{14}]$ GeV and washout parameter $K$ that depends on the light-heavy neutrino Yukawa couplings $\lambda$, in the weak ($K < 1$) and strong ($K > 1$) washout regimes. The resulting novel features compatible with observed baryon asymmetry are detectable by future experiments like LISA and ET. By estimating signal-to-noise ratio (SNR) for upcoming GW experiments, we investigate the effect of the majoron mass $M_\phi$ and reheating temperature $T_\phi$, which depends on the $\phi-N$ Yukawa couplings $y_N$.

In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom that make up a device's physical layer is used to redundantly encode a smaller amount of logical information. We elaborate this parallel in terms of quantum reference frames (QRFs), which are a universal toolkit for dealing with symmetries in quantum systems and which define the gauge theory analog of encodings. The result is a precise dictionary between QECCs and QRF setups within the perspective-neutral framework for gauge systems. Concepts from QECCs like error sets and correctability translate to novel insights into the informational architecture of gauge theories. Conversely, the dictionary provides a systematic procedure for constructing symmetry-based QECCs and characterizing their error correcting properties. In this initial work, we scrutinize the dictionary between Pauli stabilizer codes and their corresponding QRF setups. We show that there is a one-to-one correspondence between maximal correctable error sets and tensor factorizations splitting system from error-generated QRF degrees of freedom. Relative to this split, errors corrupt only redundant frame data, leading to a novel characterization of correctability. When passed through the dictionary, standard Pauli errors behave as electric excitations that are dual, via Pontryagin duality, to magnetic excitations related to gauge-fixing. This gives rise to a new class of correctable errors and a systematic error duality. We illustrate our findings in surface codes, which themselves connect quantum error correction with gauge systems. Our exploratory investigations pave the way for foundational applications to gauge theories and for eventual practical applications to quantum simulation.

We consider a stochastic spectator scalar field coupled to fermion via the Yukawa interaction, in the inflationary de Sitter background. We consider the fermion to be massless, and take the one loop effective potential found earlier by using the exact fermion propagator in de Sitter spacetime. We take the potential for the spectator scalar to be quintessence-like, $V(\phi)=\alpha |\phi|^p$ ($\alpha \ensuremath{>} 0,\ p\ensuremath{>} 4$), so that the total effective potential is generically bounded from below for all values of the parameters and couplings, and a late time equilibrium state is allowed. Using next the stochastic spectral expansion method, we numerically investigate the two point correlation function, as well as the density fluctuations corresponding to the spectator field, with respect to the three parameters of the total effective potential, $\alpha,\ p$ and the Yukawa coupling, $g$. In particular, we find that the power spectrum and the spectral index corresponds to blue tilt with increasing $g$. The three point correlation function and non-Gaussianity corresponding to the density fluctuation has also been investigated. The increasing Yukawa coupling is shown to flatten the peak of the shape function in the squeezed limit. Also in this limit, the increase in the same is shown to increase the local non-Gaussianity parameter.

A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in Quantum Chromodynamics (PRD 97 (2018) 9, 091901 PRD 109 (2024) 7, L071502), in particular in connection to mesons. This \textit{polydeterminant function}, known in the mathematical literature as a mixed discriminant, associates $N$ distinct $N\times N$ complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.

We study the boundary criticality for the Gross-Neveu-Yukawa (GNY) models. Employing interacting Dirac fermions on a honeycomb lattice with armchair boundaries, we use determinant quantum Monte Carlo simulation to uncover rich boundary criticalities at the quantum phase transition to a charge density wave (CDW) insulator, including the ordinary, special, and extraordinary transitions. The Dirac fermions satisfy a Dirichlet boundary condition, while the boson field, representing the CDW order, obeys Dirichlet and Neumann conditions at the ordinary and special transitions, respectively, thereby enriching the critical GNY model. We develop a perturbative $4-\epsilon$ renormalization group approach to compute the boundary critical exponents. Our framework generalizes to other GNY universality class variants and provides theoretical predictions for experiments.

We show that baryogenesis can arise from the cosmological evolution of a scalar field that governs CP-violating parameters, such as the Yukawa couplings and the theta terms of the Standard Model. During the big bang, this scalar may reach a CP-violating minimum, where its mass can be comparable to the inflationary Hubble scale. Such dynamics can emerge in theories featuring either a spontaneously broken local U(1) symmetry or modular invariance. The latter arises naturally as the effective field theory capturing the geometric origin of CP violation in toroidal string compactifications. Modular baryogenesis is compatible with the modular approach to resolving the strong CP problem.

We show that for Horndeski theories it is possible to derive mathematically compact consistency relations (CR) between physically observable quantities, valid for different classes of theories defined by the behavior of the brading function $\alpha_B$, independent of all other property functions. The CRs establish a parametrization independent direct relation between the effective gravitational constant, the slip parameter, the gravitational and electromagnetic waves (EMW) luminosity distances, the speed of gravitational waves (GW) and the sound speed. The no-brading CR is also satisfied by general relativity (GR), and allows to estimate the gravitational coupling from GWs observations, independently from large scale structure (LSS) observations. A general, less mathematically compact, consistency condition is also derived, valid for any form of the function $\alpha_B$ and the other property functions. We apply the CRs to map the large scale structure observational constraints on the effective gravitational constant and the slip parameter to GW-EMW distance ratio constraints, showing that LSS and GWs give independent constraints consistent with no-brading. Beside allowing to perform parametrization and model independent tests of the consistency between different constraints on modified gravity, the CRs allow to probe the value of the effective gravitational constant with multimessenger observations, independently from LSS observations.

A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the operator valued coefficients in the expansion of the $R$-matrices with respect to their spectral parameters, with the lowest order one being the Reshetikhin condition. These coefficients can be solved iteratively using Kennedy's inversion formula, which reconstructs the $R$-matrix after an infinite number of steps. For a generic Hamiltonian, the procedure could fail at any step, making the conditions useful as an integrability test. However in all known examples they all turn out to be satisfied whenever the lowest order condition is. It remains to be understood whether they are all implied by the Reshetikhin condition.

An observable spacetime can be viewed as a "continuum" of worldline coincidences (events) between a particle system and the observers of an ideal extended reference frame (RF). When this frame is absent, the metric encodes the infinitesimal proper intervals between those events that the ideal RF would assign if it were present. Extending this idea to the quantum domain -- where events arise from interactions that generate correlations -- we propose that, within a small spacelike region, the metric encodes local correlations with a quantum RF, thereby dispensing with its physical presence. This framework yields the full nonlinear Einstein equation in two scenarios: either recovering the maximal vacuum entanglement hypothesis in the first-order limit of state perturbations or producing a reference spacetime whose scalar curvature equals the cosmological constant.

We set out to compute the longitudinal magnetoconductivity for an isolated and isotropic Kramers-Weyl node (KWN), existing in chiral crystals, which forms an exotic cousin of the conventional Weyl nodes resulting from band-inversions. The peculiarities of KWNs are many, the principal one being the presence of two concentric Fermi surfaces at any positive chemical potential ($\mu$) with respect to the nodal point. This is caused by a dominant quadratic-in-momentum dispersion, with the linear-in-momentum Dirac- or Weyl-like terms relegated to a secondary status. In a KWN, the chirally-conjugate node typically serves as a mere doppelgänger, being significantly separated in energy. Hence, when $\mu$ is set near such a node, the signatures of a lone node are probed in the transport-measurements. The intrinsic topological quantities in the forms of Berry curvature and orbital magnetic moment contribute to the linear response, which we determine by exactly solving the semiclassical Bolzmann equations. Another crucial feature is that the two bands at the same KWN node carry actual spin-quantum numbers, thus providing an additional coupling to an external magnetic field ($\boldsymbol B$), and affecting the conductivity. We take this into account as well, and demonstrate that it causes a linear-in-$B$ dependence, on top of the usual $B^2$-dependence.

We develop a new class of cosmological attractors which are compatible with the recent ACT results. They are based on two types of fractional Kaehler potentials, K, for a gauge-singlet inflaton phi which reduce, along the inflationary path, to the form N/(1-phi^qM)^p with qM=1, 2 and 0.1< p<10. The combination of these K's with the chaotic potentials phi^n (where n=2, 4) within a non-linear sigma model leads to inflationary observables which are consistent with the current data and largely independent from qM and n. Endowing these K's with a shift symmetry we also offer a supergravity realization of our models introducing two chiral superfields and a monomial superpotential, linear with respect to the inflaton-accompanying field. The attainment of inflation with subplanckian inflaton values and the large values for the tensor-to-scalar ratio, which increases with N, are two additional attractive features of our proposal.

Symmetry topological field theory (SymTFT), or topological holography, offers a unifying framework for describing quantum phases of matter and phase transitions between them. While this approach has seen remarkable success in describing gapped and gapless pure-state phases in $1+1$d, its applicability to open quantum systems remains entirely unexplored. In this work, we propose a natural extension of the SymTFT framework to mixed-state phases by introducing the \textit{symmetry taco}: a bilayer topological order in $2+1$d whose folded geometry naturally encapsulates both strong and weak symmetries of the $1+1$d theory. We use this perspective to identify a series of correspondences, including a one-to-one map between intrinsically gapless SPTs (igSPTs) and certain gapped SPTs, and a mapping between igSPTs and intrinsically average SPTs (iASPTs) arising in $1+1$d mixed states. More broadly, our framework yields a classification of short-range correlated $G$-symmetric Choi states in $1+1$d, provides a route for systematically generating mixed-state SPTs via local decoherence of igSPTs, and allows us to identify a new mixed-state ``anomaly". Besides folding in mixed-state phases into the SymTFT paradigm, the symmetry taco opens new avenues for exploring dualities, anomalies, and non-equilibrium criticality in mixed-state quantum matter.

We present a field configuration-based temperature estimator in lattice gauge theories, constructed from the gradient and Hessian of the Euclidean action. Adapted from geometric formulations of entropy in classical statistical mechanics, this estimator provides a gauge-invariant, non-kinetic diagnostic of thermodynamic consistency in Monte Carlo simulations. We validate the method in compact U(1) lattice gauge theories across one, two, and four dimensions, comparing the estimated configurational temperature with the conventional temperature set by the temporal extent of the lattice. Our results show that the estimator accurately reproduces the input temperature and remains robust across a range of lattice volumes and coupling strengths. The temperature estimator offers a general-purpose diagnostic for lattice field theory simulations, with potential applications to non-Abelian theories, anisotropic lattices, and real-time monitoring in hybrid Monte Carlo algorithms.

The Macdonald operator is known to coincide with a certain element of the quantum toroidal $\mathfrak{gl}(1)$ algebra in the Fock representation of levels $(1,0)$. A generalization of this operator to higher levels $(r,0)$ can be built using the coproduct structure, it is diagonalized by the generalized Macdonald symmetric functions, indexed by $r$-tuple partitions and depending on $r$ alphabets. In this paper, we extend to the generalized case some of the known formulas obeyed by ordinary Macdonald symmetric functions, such as the $e_1$-Pieri rule or the identity relating them to Whittaker vectors obtained by Garsia, Haiman, and Tesler. We also propose a generalization of the five-term relation, and the Fourier/Hopf pairing. In addition, we prove the factorized expression of the generalized Macdonald kernel conjectured previously by Zenkevich.

This paper investigates the Teleparallel Robertson-Walker (TRW) $F(T)$ gravity solutions for a Chaplygin gas, and then for any polytropic gas cosmological source. We use the TRW $F(T)$ gravity field equations (FEs) for each $k$-parameter value case and the relevant gas equation of state (EoS) to find the new teleparallel $F(T)$ solutions. For flat $k=0$ cosmological case, we find analytical solutions valid for any cosmological scale factor. For curved $k=\pm 1$ cosmological cases, we find new approximated teleparallel $F(T)$ solutions for slow, linear, fast and very fast universe expansion cases summarizing by a double power-law function. All the new solutions will be relevant for future cosmological applications on dark matter, dark energy (DE) quintessence, phantom energy, Anti-deSitter (AdS) spacetimes and several other cosmological processes.

We present an upgraded formula for Wigner function and spin polarization of fermions emitted by a relativistic fluid at local thermodynamic equilibrium at the decoupling which improves the one obtained in refs. [1, 2] and used in numerical simulations of relativistic nuclear collisions. By using a new expansion method, applicable to decoupling hypersurfaces with arbitrary geometry, we reproduce the known term proportional to thermal vorticity and obtain an upgraded form of the spin-shear term which captures the dependence on the geometry. The new method also includes additional contributions whose physical nature is to be assessed. The new expression also naturally excludes contributions from space-time gradients in the normal direction of the hypersurface, providing a theoretical justification for the isothermal condition previously imposed a priori. This framework can be extended to particles with arbitrary spin.