Papers

Logarithmic correction to BPS black hole entropy, computed from microscopic description, often contains terms involving large ratios of charges, besides the logarithmic terms involving the overall scale of the charges. If the electric charges are much larger than the magnetic charges, then the attractor value of the string coupling is small and one might hope to use weakly coupled string theory to compute logarithmic corrections involving ratios of charges from the macroscopic side. We compute these for black holes in flat space-time, preserving four supercharges, in $\mathcal{N} = 2$, $\mathcal{N}=4$ and $\mathcal{N}=8$ supersymmetric string compactifications in four dimensions. We find perfect agreement with the microscopic results in $\mathcal{N}=4$ and $\mathcal{N}=8$ theories, for which the microscopic results are known. Various stringy and statistical mechanical effects become important in this analysis, including 1) use of the correct ultra-violet cut-off (string scale instead of Planck scale), 2) correct path integral measure (ultra-local measure with appropriate dilaton dependent metric), 3) use of the correct path integral variable (Kalb-Ramond 2-form instead of the dual axion) and 4) change of ensemble (from grand canonical to microcanonical). We also verify that the measure we use is consistent with what follows from the BV formalism of string field theory.

We present an $SU(12) \times SU(2)_L \times U(1)_R$ model unifying $SU(9)$ quark color-flavor with $SU(3)$ lepton flavor as a flavorful alternative to conventional theories of unification. We begin in the ultraviolet with a single yukawa shared by the unified up-type quarks and neutrinos, and no further new fermions. We show that gauged quark color-flavor and lepton flavor instantons dynamically generate the bottom and tau yukawas, which implements a massless quark solution to the strong CP problem and sets up a flavored type-I seesaw mechanism. Only two new scalar irreps are needed for the symmetry-breaking steps, which include quark color-flavor deconstruction and then infrared reunification, and the Standard Model gauge group in this theory emerges as \[G_{\rm SM} = \frac{SU(3)_C \times SU(2)_L \times U(1)_Y \times \mathbb{Z}^X_{18}}{\mathbb{Z}_{3} \times \Gamma \times \mathbb{Z}_3},\] where $\Gamma \in \lbrace 1, \mathbb{Z}_2 \rbrace$ is the electroweak global structure and there is a discrete gauge symmetry $X = B - 3(L_i + L_j - L_k)$ which brings additional $\mathbb{Z}_3$ global structure to the SM. This gauge symmetry acts as a flavorful upgrade of the $\mathbb{Z}^{B+L}_{18}$ anomaly-free global symmetry of the SM and stabilizes the proton absolutely. Non-invertible chiral symmetry-breaking is crucial to our model, and we discuss the rich spectrum of emergent generalized symmetries and topological defects appearing at various stages. In the infrared, the novel shared quotient between continuous and discrete groups links the one-form and two-form global symmetries of the Standard Model.

We show that axions cause extremal black holes to have singular horizons. This is true for almost all values of the axion mass and coupling provided the black hole is rotating and has some arbitrarily small nonzero charge. When the axion mass becomes large, these singularities are related to the recently discovered singularities induced by higher-derivative corrections to the Einstein-Maxwell equations. Away from extremality, this effect produces anomalously large tidal forces in the vicinity of near-extremal horizons, causing breakdown of the effective theory.

We put forward a quantum model of cosmology that is exactly periodic but avoids the Boltzmann Brain problem. If the universe is described by a quantum state evolving unitarily in a finite-dimensional Hilbert space, its evolution will be recurrent: given enough time, the state will return arbitrarily close to its initial state. There is a worry that such a scenario cannot be phenomenologically acceptable, because the state will spend most of its time in a high-entropy equilibrium macrostate, with rare fluctuations downward in entropy, and the vast majority of observers will be minimal fluctuations away from equilibrium, or “Boltzmann Brains." Here we show that this is not necessarily true. If the differences in energy eigenvalues are commensurable, the evolution is not simple recurrent, but exactly periodic. Moreover, if the state starts at minimum thermodynamic entropy, its evolution can feature a distinguished entropy excursion that is much more pronounced than one would expect from the conventional expression $P(\Delta S) \propto \exp(-\Delta S)$. This excursion could represent our Big Bang, with relatively few Boltzmann fluctuations occurring in the subsequent equilibrium phase before a Big Crunch occurs and the cycle begins again. We speculate on the spacetime interpretation of this kind of quantum universe.

We investigate a planar Dirac oscillator coupled to a spatially uniform \(\utwo=\uone\times\su\) Yang–Mills background. The gauge configuration, adapted from the Dossa–Avossevou construction, contains an Abelian magnetic field \(B\), a non-Abelian spatial amplitude \(\beta\), and a non-Abelian scalar amplitude \(\rho\). Within the Pauli-reduced formulation, the non-Abelian field strength produces a constant operator on \(\mathbb{C}^{2}_{\mathrm{spin}}\otimes\mathbb{C}^{2}_{\mathrm{iso}}\). This operator contains a diagonal internal-Zeeman contribution proportional to \(\sigma^{3}T^{3}\) and an off-diagonal spin–isospin term proportional to \(\sigma^{1}T^{1}+\sigma^{2}T^{2}\). Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues \[ \lambda_{\mathrm{FM}}=\frac{g^{2}\beta^{2}}{4m},\qquad \lambda_{S}=-\frac{g^{2}\beta(\beta-2\rho)}{4m},\qquad \lambda_{T}=-\frac{g^{2}\beta(\beta+2\rho)}{4m}. \] Consequently, the aligned internal-Zeeman scale is quadratic in \(\beta\), whereas the singlet–triplet separation is linear in \(\beta\rho\). The revised formulation makes the sign conventions explicit, verifies the main limiting cases, distinguishes the Pauli-reduced spectrum from a full first-order Dirac diagonalization, and clarifies the physical meaning of the numerical illustrations.

We introduce a boundary–residue incidence coalgebra associated with the face poset of a positive geometry and apply it to associahedral scattering forms. The construction is motivated by the analogy between the Connes–Kreimer coproduct on Feynman graphs and the recursive residue structure of canonical forms. For the Stasheff associahedron \(K_n\), whose faces are indexed by non-crossing dissections of an \((n+1)\)-gon, we prove that the incidence coproduct records all intermediate nested planar factorisation channels of the corresponding tree-level scalar amplitude. The residue of the canonical form on a face labelled by a dissection factorises as the exterior product of canonical forms on the lower associahedra associated with the resulting subpolygons. We illustrate the construction explicitly for the pentagon associahedron \(K_4\), corresponding to the five-point planar scalar amplitude. We then formulate a loop-level extension: whenever a planar loop integrand is represented by a positive geometry, the associahedral face poset is replaced by the boundary poset of the corresponding loop geometry. The one-loop halohedron gives a concrete scalar example, while in the non-planar case we define the associated incidence coalgebra at the level of logarithmic singularity strata. Finally, we compare the boundary–residue coalgebra with the cellular incidence coalgebra of a triangulated or regular CW spacetime. The face poset of a finite regular CW complex reconstructs its barycentric subdivision, and hence its underlying polyhedron, while in positive geometry the same incidence mechanism organises canonical-form residues. This yields an incidence-first bridge between cellular spacetime topology and positive-geometric amplitude factorisation, without assuming that metric or causal data are determined by topology.

Global symmetry anomalies of a quantum field theory (QFT) can be packaged as specific couplings of a higher-dimensional symmetry theory (SymTh). In this work we show that for 5D superconformal field theories (SCFTs) engineered from M-theory backgrounds $X$ a Calabi-Yau cone, this data can be extracted from the path algebra of branes probing $X$. This provides a complementary algebraic approach compared with more geometric computations based on the explicit calculation of triple intersection numbers in a resolved geometry and / or $\eta$-invariants extracted from the boundary geometry $\partial X$. Our method applies in situations where the counterpart geometric computation is either unknown or combinatorially unwieldy. We illustrate with several toric threefold examples, including orbifolds $\mathbb{C}^{3} / \Gamma$ and more general non-orbifold Calabi-Yau cones of Sasaki-Einstein five-manifolds.

Self-dual theories, being UV-finite, should have their own AdS/CFT dualities. Higher-spin extensions of self-dual theories are attractive to simplify the CFT duals. The maximal self-dual theory is Chiral higher-spin gravity, which should be dual to a subsector of Chern–Simons matter theories. As a step toward establishing self-dual holography, we develop the Fefferman–Graham expansion and holographic dictionary for arbitrary spin self-dual theories. As an application, we derive bulk-to-bulk propagators and compute three- and four-point AdS/CFT correlators in a contraction of Chiral higher-spin gravity, which is a higher-spin extension of self-dual Yang–Mills theory.

The existence of a landscape of metastable vacua raises the possibility that our Universe may have undergone quantum vacuum decay at late times. This work explores how such a transition can be tested with cosmological observables, focusing on precision distance measurements and cosmic microwave background (CMB) anisotropies. A set of phenomenological models is constructed in which late-time quantum tunneling changes the vacuum energy and may convert a subcomponent of dark matter into dark radiation, possibly accompanied by domain-wall production. The resulting expansion histories are compared with DESI DR2 baryon acoustic oscillation data; supernova distance measurements from DES-Dovekie, Pantheon+, and Union3; and a compressed CMB likelihood. For quantum-tunneling models, current cosmological distance measurements still allow a 50% decrease in the total vacuum energy for a transition redshift $z_t<1$. The model with dark-matter conversion and domain-wall production provides a good fit to resolve the tension between cosmological observables and the $\Lambda$CDM model, with a preferred transition around $z_t \sim 7$ and about 10% of dark matter participating in the transition. Additionally, CMB anisotropy constraints from bubble nucleation and the associated domain-wall network are derived and shown to strongly restrict slow or sparse late transitions. Applied to the minimal quantum-tunneling model, these constraints allow an $\mathcal{O}(10\%)$ decrease in the total vacuum energy for a transition redshift $z_t$ of order unity. For nonminimal models, dark-matter-density-dependent tunneling can proceed rapidly enough to evade such bounds. These results demonstrate that late-time quantum vacuum decay is a testable cosmological phenomenon and provide a concrete observational handle on metastable-vacuum physics motivated by landscape scenarios.

We study the primary constraint structure of Newer General Relativity, a gravity theory based on a torsionless teleparallel geometry. The gravitational action is built from a scalar formed by quadratic combinations of the nonmetricity tensor, with arbitrary coefficients $c_i$ in the Lagrangian. We decompose the Lagrangian and compute the canonical momenta conjugate to the metric. We characterize the primary constraints arising from these momenta by identifying when the map between velocities and momenta becomes non-invertible, and organize the outcome through a fully nonlinear decomposition into scalar, vector and tensor sectors. Comparing with previous results in the literature, we recover five and three primary constraints associated with the tensor and vector sectors, respectively. We also identify a previously unreported degeneracy in the scalar sector, which yields either one or two scalar primary constraints depending on the conditions imposed on the parameters $c_i$. Finally, we obtain the primary constraints associated with the covariant formulation of symmetric teleparallel gravity.

In this paper, we present HyperPrecision, a Mathematica package for high-precision numerical evaluation of general Horn-type multivariate hypergeometric functions and their Laurent expansions in a small parameter $\epsilon$. Such functions appear widely in physics and mathematics, with applications ranging from quantum field theory and string theory to number theory and statistics. Their high-precision numerical evaluation, however, remains challenging, since their defining series converge only in restricted domains and analytic continuation beyond these domains is, in general, non-trivial. HyperPrecision addresses this problem by automatically constructing the Pfaffian system of partial differential equations for a given hypergeometric function and restricting it to a one-dimensional contour in the space of variables connecting the starting to the target point. The resulting ordinary differential equation is then solved by the Frobenius method, with boundary conditions fixed analytically by the defining series. We illustrate the use of the package by evaluating commonly occurring multivariate hypergeometric functions, including the Appell $F_1$, $F_2$, $F_3$, and $F_4$ functions, the Horn $G$- and $H$-series, and the Lauricella $F_A$, $F_B$, $F_C$, and $F_D$ functions, as well as by considering applications to angular integrals, Feynman integrals, and cosmological and holographic correlators.

We present a lattice QCD determination of the Mellin moments of the unpolarized gluon parton distribution function in the proton. The analysis is based on matrix elements of nonlocal gluon operators coupled to momentum-boosted proton states. The calculation relies on an $N_f=2+1+1$ ensemble of maximally twisted mass fermions with clover improvement and the Iwasaki-improved gauge action, at a pion mass of approximately 260 MeV. Working within the short-distance operator product expansion (OPE) of the reduced gluon Ioffe-time distribution, we extract ratios of higher-order gluon moments, $\langle x^n\rangle$ with $n>1$, to the gluon momentum fraction, $\langle x\rangle$. We investigate systematic effects associated with the truncation of the order of moment in the OPE, the choice of minimum and maximum Wilson-line separations entering the analysis, and the treatment of mixing with the quark-singlet under perturbative matching. The stability of the extracted moments is further studied under scale evolution using DGLAP equations, allowing us to assess uncertainties related to perturbative truncation by varying the scale. Our work provides a determination of the ratio $\langle x^3\rangle_g/\langle x\rangle_g$ at a scale of 2 GeV, with uncertainties that account for both statistical and the dominant theoretical systematic uncertainties.

The charged Reissner Nordstr$\"{o}$m black hole metric is obtained from the Einstein Hilbert action. This action has the kinetic term $F^2 = (da)^2$. Motivated by the higher-form symmetry structure of the EFT of Force Free Electrodynamics, we replace the Maxwell field-strength in the EH action by the gauge-invariant combination $(b-da)^2$, where $a_\mu$ is the gauge field and $b_{\mu\nu}$ is a background two-form field which is closed, that is, $db =0$. This ensures that the new action has a higher form symmetry $b \rightarrow b+d\Lambda, a\rightarrow a+\Lambda$. Here, unlike in qed, $\Lambda$ may be any one form (not necessarily a differential one form $\partial_\mu \phi$). The higher form symmetry here is one with the conserved current being a two form and the charge integrated on surfaces. It is the current of vector field lines that is conserved here, not the current of particles. Thus, integrating over a surface through which the field lines pierce is sufficient to find the number of these lines that are passing through; so the charge is integrated on surfaces, rather than on the volume. By fixing a gauge for $a_\mu$ and $b_{\mu\nu}$, we obtain the black-hole metric dual to the boundary theory of FFE. There are two different starting points: 1)Consider the $b$ to be exact. The bulk dual to this theory is the RN geometry. 2)Consider the $b$ to have a Dirac Like Monopole and thus to not be exact ($b \neq dc$ for any $c$). This again does not lead to a new bulk dual, it leads us to the Dyonic RN geometry (which arises in the E-M theory when $a$ has the monopole term). Thus, Einstein-FFE leads to the known RN and dyonic solutions of the E-M theory. We note that AdS-CFT applied to this problem states that since the boundary EFT of FFE describes the same theory of a sector of strongly magnetised QED plasma, bulk E-FFE reproduces the same solutions of E-M theory.

We introduce a one dimensional spin $\frac{1}{2}$ Hamiltonian with multi-site interactions, but still local. The algebra of its Hamiltonian densities resembles that of the transverse field Ising model. Using this fact we show that its spectrum is free-fermionic but with a huge degeneracy for each level. The source of the degeneracy is a set of local conserved quantities that act like a classical background field for the quantum system. The thermodynamics of this system is contrasted with the standard Ising model. At the gapless points in the energy spectrum, we show that this system can be derived from the quantum inverse scattering method adapted to a multi-site generalization of the Yang-Baxter equation as introduced by E. Rowell and Z. Wang. The $R$-matrix is constructed using generators of extraspecial 2-groups. This helps us extract all the conserved charges and lay the framework for a general mechanism to generate such multi-site interaction spin systems that are transverse field Ising models under the hood. A remark on how to obtain P. Fendley's free-fermion in disguise models in this formalism is also included.

This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented surfaces and in the presence or absence of a cosmological term, explicit presentations of the corner algebras are obtained in terms of generators and relations, identifying them as infinite-dimensional oscillator-type Lie algebras with an abelian summand. A construction of infinite families of simple modules via bosonic Fock space representations is provided. In the non-abelian case on the torus, the corner algebras are described as quotients constructed from the central extensions of double-loop algebras over certain non-semisimple Lie algebras. A construction of infinite families of simple Fock-type modules of the free corner algebra via an induced module procedure is also provided. The resulting modules descend only trivially to the physical quotient, revealing an obstruction in the present construction in the non-abelian setting.

We develop a perturbative, diagrammatic framework for constructing Nicolai maps and apply it to four-dimensional $\mathcal{N}=1$ Poincaré supergravity expanded around flat Minkowski space. It provides an alternative to the coupling-flow-operator construction, which faces several obstructions when extended to local supersymmetry. Expanding the bosonic effective action and the Nicolai map jointly in the gravitational coupling $\kappa$ and the loop-counting parameter $\hbar$, we derive the Nicolai-map defining conditions, i.e. the free-action and determinant-matching conditions, order by order. The diagrammatics enumerates all admissible local terms in the Nicolai-map ansatz from the effective-action diagrams and reduces the construction to a finite system of nonlinear polynomial equations. Carried through order $\kappa^{2}$, the resulting constraints are found to be independent of the detailed bosonic input and hierarchical, order-$\kappa^{2}$ consistency further restricting the order-$\kappa$ data. A consistent Nicolai-map construction for the Einstein–Hilbert graviton sector is found to require the Rarita–Schwinger gravitino already at this order: Einstein gravity admits a Nicolai map only through its $\mathcal{N}=1$ supersymmetric completion, Poincaré supergravity, supporting Nicolai's characterization of supersymmetry.

We investigate the geodesic structure and optical appearance of compact objects with primary scalar hair in shift- and parity-symmetric beyond Horndeski gravity. The analytic solution considered here depends on a theory parameter and a dimensionless mass parameter \cite{Bakopoulos:2023sdm}. For a fixed theory parameter, varying the mass traces a family of static spacetimes that can interpolate between timelike naked singularities, regular solitons, regular black holes, Reissner-Nordström-like black holes, multi-horizon black holes, and Schwarzschild-like black holes. We classify these branches by their horizon structure and analyze null and timelike geodesics, focusing on light rings, innermost stable circular orbits, and static spheres. We then compute thin-disk optical images by ray tracing. We find that the number of horizons is not directly encoded in the image: horizonless objects can show shadow-like central depressions, while multi-horizon black holes can closely resemble single-horizon black holes when their exterior light ring and disk structures are similar. Thus, the optical appearance is governed mainly by the photon potential and the disk inner edge, with the deeper horizon structure leaving only an indirect imprint. Quantitative radial-profile diagnostics confirm that the degeneracy is mainly morphological: the profiles differ at fixed impact parameter, but become much closer after rescaling by the critical impact parameter. These results provide a concrete example of how distinct compact object branches in beyond Horndeski gravity can share similar observational signatures.

We study the quantum chaos bound in the photon ring region surrounding black holes. By evaluating the Lyapunov exponent associated with unstable null geodesics in a broad class of generalized Kerr geometries, as well as the temperature induced by a string probe, we show that the quantum chaos bound is exactly saturated on equatorial circular orbits of the photon ring. We confirm our result by deriving the same exponent from out-of-time-order correlators in the near ring region. As a byproduct, we show that the photon ring saturation of the quantum chaos bound implies the saturation of the Bekenstein bound on the rate of information emission from the ringdown phase through the quasi-normal modes in the eikonal limit. Our results extend the known correspondence between black hole thermodynamics and chaotic dynamics, highlighting the role of the photon ring as a probe of the fundamental limits on thermalization and information scrambling in black holes.

We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible affine vertex algebras as well as admissible W-algebras associated with nilpotent elements of standard Levi type, we prove the holonomicity of the sheaf of conformal blocks over the moduli space of bundles. Furthermore, we show that the space of flat sections of the associated Jacobi-invariant connection is spanned by trace functions on modules. This result provides a substantial generalization of the celebrated theorem of Yongchang Zhu to quasi-lisse vertex algebras. As a special case, we deduce that for affine vertex algebras at admissible level, the dimension of the space of conformal blocks coincides with the number of admissible weights at that level.

We propose gate-parameter Lee-Yang zeros of Loschmidt amplitudes as probes of dynamical phases in finite quantum circuits. We study Floquet circuits constructed from two-qubit fSim gates with identical parameters, for which the Loschmidt amplitude becomes a rational function of the gate parameters after a suitable change of variables. At fixed system size and large circuit depth, the zeros in one complexified gate parameter, with the other held fixed, condense onto limiting curves. In contrast to conventional Loschmidt or Fisher zeros in complex time, these zeros live directly in the complex plane of a tunable gate parameter. We show that the limiting set has two origins: a state-dependent component controlled by overlaps with Floquet eigenstates, and a universal component fixed by the Floquet spectrum. As the remaining gate parameter is varied, the universal zero set reorganizes abruptly, providing a finite-qubit diagnostic of a dynamical phase transition. We demonstrate this behavior in a Bethe ansatz solvable brickwork circuit and in longer-range fSim circuits outside this solvable structure. The mechanism follows from the Beraha-Kahane-Weiss theorem together with local unitarity, and is therefore spectral rather than a special consequence of integrability.

Massive spinor-helicity variables in four dimensions are a useful tool for studying amplitudes between higher-spin fields and gravitons. Among them a special, simple set of amplitudes reproduces the linearized stress-energy tensor of a Kerr black hole in the classical limit. In this work we initiate the study of the classical limit of three-point spinor-helicity amplitudes in five dimensions. We introduce the map between the spinor invariants and the expectation values of spin operators and match the amplitude building blocks with those of the multipole expansion. Interestingly, in order to take the classical limit of a general amplitude, we need to augment the multipole structures with the Hodge dual of the classical spin tensor. We study the classical limit of alternative spinning states not described by fully-symmetric products of polarisations and conclude that they can describe the same spacetimes. Finally, by relaxing the orthogonality condition of the spin tensor we are able to model spacetimes with a single rotational isometry and match these to the classical limit of amplitudes allowing for an internal spin shift. Along the way we also identify the class of amplitudes describing the Myers-Perry black hole and comment on its generalization to arbitrary dimensions.

The $N$-color Ashkin-Teller model corresponds to $N$ Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the solutions of the exact renormalization group fixed points equations. The weak disorder sector is characterized by a solution that, for any fixed $N$ larger than 1, is a line of fixed points with Ising thermal exponents and continuously varying magnetic exponents. The number of fixed point solutions allowed by the symmetries of the model increases at strong disorder illustrating the growing dependence on the distributions of the two random couplings. The presence of some critical exponents which do not depend on the symmetry parameter $N$ confirms this type of superuniversality as a peculiar feature of random criticality.

Magic relations are a class of integration-by-parts identities where all integrals in the generating sector drop out. Since their presence causes several otherwise successful methods in the Feynman-integral computational pipeline to break down, they are important to detect and understand. In this paper, we take a first step toward a systematic characterization of such identities. Specifically, we observe and argue that the occurrence of magic relations always coincides with the presence of higher-dimensional critical varieties in the generating sector. This provides a practical computational test to check if a family of Feynman integrals can contain magic relations and to find them, which we implement in the ancillary Mathematica file Magic-Test.m. Additionally, we discuss how to count the number of master integrals in the presence of higher-dimensional critical varieties, classify the behavior of magic relations under symmetries, and we discuss their interplay with cuts.

Starting from the exact Projected Central Limit Theorem on hyperspheres, we rederive the Beta distribution for subsystem occupation probabilities and Lubkin's purity formula from elementary hyperspherical moments, quantifying the finite-size “platykurtic” suppression of tails relative to the Gaussian approximation used in standard eigenstate-thermalization and typicality treatments. Our main new result concerns the bipartite quantum mutual information $\langle I(A{:}B)\rangle$ for Haar-random pure states. We show that its full asymptotic expansion in $1/N$ admits a Bernoulli-factorized form in which every order $k \ge 1$ carries the symmetric factor $(d_A^{2k}-1)(d_B^{2k}-1)$ and all higher odd-order corrections vanish identically. Through an exact algebraic reorganization of Page's formula (conjectured in Ref.~\cite{Page1993} and subsequently proven~\cite{Foong1994, SanchezRuiz1995, Sen1996}), we establish that the leading finite-size correction separates into a dominant $\mathfrak{su}(d_A) \otimes \mathfrak{su}(d_B)$ bipartite quantum coherence contribution $(d_A^2 - 1)(d_B^2 - 1)/(2N)$ and a subtracted classical-probability (Cartan $\otimes$ Cartan) contribution $(d_A - 1)(d_B - 1)/(2N)$, and we trace this separation to the difference between diagonal and eigenvalue entropies via Schur's majorisation theorem, with the dimensional counts $(d-1)$ and $(d^2-1)$ acquiring meaning through the Cartan structure of the generalised Bloch decomposition. These results admit a single non-perturbative closed form: the exact typical mutual information factors as $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, with $\mathcal{G}$ given by an explicit Bose–Einstein integral whose asymptotic expansion in $1/N$ reproduces the Bernoulli series.

The average bipartite quantum mutual information $\langle I(A{:}B)\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative closed form: $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, where $\mathcal{G}$ is given by an explicit convergent integral over a Bose–Einstein kernel. The overall factor $(d_A^2-1)(d_B^2-1)=\dim[\mathfrak{su}(d_A)]\cdot\dim[\mathfrak{su}(d_B)]$ is exact, not merely asymptotic. The asymptotic expansion of $\mathcal{G}$ in $1/N$ yields a Bernoulli-factorised series whose coefficients involve $\zeta(1{-}2k)$; this series diverges, and our integral is its exact Borel sum. The integral representation also makes $\langle I\rangle < (d_A^2{-}1)(d_B^2{-}1)/(2N)$ manifest via a scale-inversion symmetry of the kernel. Our derivation traces the mutual information's structure to an exact decomposition of Page's entropy into a diagonal (Dirichlet) contribution and a Schur-majorisation eigenvalue correction, whose assembly into the mutual information cleanly separates classical from quantum correlations.

We study the thermodynamics of the symmetry-improved Cornwall-Jackiw-Tomboulis (SICJT) formalism and apply it to a low-energy effective theory of QCD. In the symmetry-improved formulation, Ward-Takahashi identities are restored by auxiliary sources whose values are fixed self-consistently by the equilibrium state. While this construction improves the symmetry properties of the loop-wise truncated two-particle-irreducible (2PI) theory, it also makes the thermodynamic interpretation of the pressure nontrivial. We formulate several pressure prescriptions, including the conventional vacuum-subtracted pressure, a source-matched subtraction, and a pulled-back pressure in which the explicit source-induced energy shift is removed. Using the three-flavor linear sigma model with quarks, we analyze the equation of state, isentropic trajectories, adiabatic sound velocity, and trace anomaly across the chiral transition. We find that the global thermodynamic structure is stable under the different prescriptions, while quantitative differences are concentrated near the crossover and first-order transition region. These results establish a practical framework for constructing thermodynamically consistent observables in symmetry-improved 2PI approaches.

We present a quantum-field-theoretic treatment of massive chiral fields in which particles possess well-defined chirality and helicity. This framework reproduces the chiral oscillation formula previously obtained in first-quantized approaches and provides a consistent description of weak-interaction processes. We further derive corresponding chiral-energy uncertainty relations.

A non-Abelian gauge field framework is proposed using the hypercomplex ring formalism. This extension generates non-compact hyperbolic symmetries, which, alongside the compact gauge symmetries, double the internal degrees of freedom. This will enable the description of bipartite gauge systems and demonstrate how field dissipation operates at the dynamical level. Working within a commutative ring allows for the decoupling of the algebraic structures and facilitates the construction of solutions to the equations of motion.

We show that in any $2n+2$ dimensions, the higher Chern-Simons action built from a semistrict Lie 2-algebra gives a non-trivial higher Wess-Zumino-Witten (WZW) term under a higher gauge transformation. The key point is that the non-zero Jacobiator directly generates the higher WZW term, whereas it vanishes when reduced to the strict case.

Timelike Liouville field theory is a candidate model for positive curvature two-dimensional quantum gravity, but a mathematically controlled Lorentzian formulation has remained elusive. In this paper we construct the theory on the cylinder $\mathbb{R}\times \mathbb{S}^1$ in the integer screening sector for a natural algebra of renormalized exponential observables. Starting from a renormalized finite-volume torus regularization, we construct infinite-volume Euclidean correlation functions, prove analytic continuation in the time variables, and identify the resulting Lorentzian boundary values by explicit contour formulas. This yields exact Lorentzian correlators for a natural class of exponential observables. We then prove locality: spacelike separated vertex operators commute in the Lorentzian theory. For smeared observables generated by the integer-charge fields $e^{2nb\phi}$, these Lorentzian expectation values define a vacuum functional on an ordered $*$-algebra and support an AQFT-type quantization without positivity. More precisely, we obtain isotone local algebras, a complete locally convex space $\mathcal H$ with dense algebraic subspace $\mathcal H_0$ carrying a nondegenerate Hermitian form (shown to be indefinite for $b<8^{-1/2}$), a continuous cyclic representation, operator-topologically closed represented local algebras, an action of cylinder translations by continuous linear homeomorphisms, and locality for the represented local net. The construction does not produce a Hilbert space or a Haag-Kastler net of local von Neumann algebras in the usual sense, but it shows that a substantial part of the Euclidean-to-Lorentzian and algebraic reconstruction mechanism survives in this nonpositive setting for timelike Liouville theory on the cylinder.