1779 papers
This paper constructs the first scaling limit of a non-Abelian lattice Yang-Mills theory in dimensions higher than two by demonstrating that, under specific gauge fixing and coupling limits, the Yang-Mills-Higgs model converges to a massive Gaussian field, thereby providing the first rigorous proof of mass generation via the Higgs mechanism in such a setting.
This paper rigorously establishes the ultraviolet finiteness of topological-holomorphic field theories on and proves that quantum anomalies vanish—specifically for odd loops when and entirely when —thereby enabling the construction of a factorization algebra structure for their quantum observables.
This paper establishes that within a fixed connectivity class, the spectral support minimizing the average intensity of a focusing Nonlinear Schrödinger equation soliton condensate containing a prescribed anchor set is a compact set composed of critical trajectories of a quadratic differential derived from the associated hyperelliptic Riemann surface.
This paper mathematically justifies the physical view of the Toda lattice at thermal equilibrium as a dense collection of soliton-like quasiparticles by rigorously defining their locations, approximating local charges and currents, and proving an asymptotic scattering relation based on the spectral properties of the system's random Lax matrix.
This paper establishes a rigorous mathematical framework for Gaussian random variables with negative variance to prove the timelike DOZZ formula for 3-point correlation functions and derive expressions for -point functions in timelike Liouville field theory, demonstrating their convergence to correct semiclassical limits.
This paper introduces a unitary transform generalizing the Fourier transform to characterize the space associated with the confluent hypergeometric kernel, establishing a Paley-Wiener theorem that proves the corresponding Wiener-Hopf operator is unitarily equivalent to the standard one and provides explicit formulas for the hierarchical decomposition of the induced operator's image.
This paper establishes a central limit theorem for additive functionals of the determinantal point process with the confluent hypergeometric kernel as the scaling parameter tends to infinity, proving their convergence to a Gaussian distribution with a quantitative bound on the Kolmogorov-Smirnov distance derived from an exact identity for multiplicative functionals.
This paper classifies positive traces on the Coulomb branch algebras of specific three-dimensional and four-dimensional gauge theories, focusing on quantizations of type Kleinian singularities and algebras associated with pure and gauge theories.
This paper establishes the previously unavailable matrix product solution for the steady state of the harmonic process by demonstrating its derivation from and clarifying its relationship to existing closed-form and nested integral representations found in recent literature.
This paper establishes the asymptotic behavior of the ground state energy for a dilute, repulsive spin-J Fermi gas in one dimension, demonstrating that it is determined by the ground state energy of an associated spin chain, specifically the Heisenberg antiferromagnet for spin-1/2 fermions.
This paper establishes a Gessel-type expansion in Jack polynomials for multiplicative functionals in the circular -ensemble, which enables the proof of Szegő-type limit theorems for and a Soshnikov-type central limit theorem for the sine- process across the full regularity class.
This paper establishes that shock formation in general first-order strictly hyperbolic systems in one spatial dimension is locally self-similar and universal, mirroring the behavior of the inviscid Burgers' equation, and derives an analytical formula for this universal solution.
This paper introduces first-order noncommutative corrections to Einstein-nonlinear electrodynamics using a Drinfel'd twist and Seiberg-Witten map, deriving perturbative solutions for static, spherically symmetric dyonic black holes that account for both intrinsic electromagnetic nonlinearity and noncommutative geometric effects.
This paper establishes the equivalence between generalised Schur partition functions of 4d $USp(2N)$ gauge theories and vector-valued modular forms by proving they satisfy specific modular linear differential equations, while also proposing extensions and conjectures linking these functions to quantum monodromy traces and 2d rational conformal field theory characters.
This paper demonstrates that the scaling behavior of Synge's world function and the van Vleck determinant changes drastically when emanating from a singular point rather than a regular one, thereby revealing the non-trivial classical structure of spacetime singularities and offering a new tool for investigating their quantum properties.
This paper investigates efficient methods for determining optimal time windows to compute covariant Lyapunov vectors in conservative Hamiltonian systems, revealing that long backward evolution intervals degrade center subspace accuracy due to vector alignment and proposing an adapted algorithm to mitigate this issue.
These lectures explore two correspondences between gauge theories and integrable many-body systems, linking gauge-theoretic dynamics to Calogero–Moser-type systems through infinite-dimensional Hamiltonian reduction and supersymmetric instanton counting, with a focus on SU(N) theories across dimensions one to six.
This paper provides a structural explanation for the success and failure of the Bethe Ansatz by identifying interaction propagation as the governing mechanism, where exact solvability arises when propagation terminates finitely without encountering structural boundaries, while its breakdown occurs when such boundaries generate irreducible interaction data that prevent finite factorization.
This paper develops the direct and inverse spectral theory for finite Hermitian banded matrices using matrix orthogonal polynomials to explicitly reconstruct matrices from spectral data, establish conditions for valid spectral measures, and explore connections to block tridiagonalization algorithms and the Toda lattice evolution.
This paper characterizes pairwise interactions satisfying the Seidl conjecture for symmetric multimarginal optimal transport and rigorously demonstrates that, for electrons in a quantum ring, the adiabatic connection potential converges to a regular Kantorovich potential in the strongly interacting limit.