math-ph papers | Gist.Science

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

Electromagnetic wave propagation in static black hole spacetimes: an effective refractive index description in Schwarzschild geometry

This paper presents a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static black hole spacetimes that reduces both axial and polar sectors to a unified master equation, enabling the derivation of a closed-form, position- and frequency-dependent effective refractive index in Schwarzschild geometry to provide an intuitive optical framework for analyzing gravitational effects on wave dynamics.

Abdullah Guvendi, Omar Mustafa Semra Gurtas Dogan, Hassan Hassanabadi2026-04-10⚛️ gr-qc

Collective Dynamics of Vortex Clusters on a Flat Torus: From Pair Interactions to a Quadrupole Description

This paper establishes a Hamiltonian framework for vortex clusters on a flat torus using the Schottky-Klein prime function, deriving a universal small-cluster expansion that reduces collective dynamics to a closed description governed by a single complex quadrupole moment, a prediction validated by numerical simulations.

Aswathy KR, Rickmoy Samanta2026-04-10🔬 physics

Resurgence of high-energy string amplitudes

This paper analyzes the fixed-angle high-energy limit of $n$ -point tree-level string amplitudes through diverse mathematical frameworks, revealing that their asymptotic structure is governed by Bernoulli numbers rather than multiple zeta values, and utilizes resurgence theory to construct transseries that unify low- and high-energy expansions while providing a new double-copy representation for closed-string amplitudes via twisted de Rham theory.

Xavier Kervyn, Stephan Stieberger2026-04-10⚛️ hep-th

The $\mathcal{N}=1$ Super-Grassmannian for CFT $_3$ and a Foray on AdS and Cosmological Correlators

This paper constructs a manifestly superconformal $\mathcal{N}=1$ Super-Grassmannian integral representation for 3D SCFT correlators that algebraically relates component functions, enabling the derivation of (A)dS $_4$ boundary correlators from exchange-only contributions and confirming consistency with flat-space limits.

Aswini Bala, Sachin Jain, Dhruva K. S., Adithya A Rao2026-04-10⚛️ hep-th

Super-Grassmannians for $\mathcal{N}=2$ to $4$ SCFT $_3$ : From AdS $_4$ Correlators to $\mathcal{N}=4$ SYM scattering Amplitudes

This paper introduces a Super-Grassmannian formalism for $\mathcal{N}=2$ to $4$ three-dimensional superconformal field theories that makes super-conformal and $R$ -symmetry constraints manifest, successfully reproducing AdS $_4$ correlators and demonstrating a direct connection to flat-space $\mathcal{N}=4$ SYM scattering amplitudes through a specific CPT self-conjugate super-operator construction.

Aswini Bala, Sachin Jain, Dhruva K. S., Adithya A Rao2026-04-10⚛️ hep-th

Vacuum-induced current density from a magnetic flux threading a cosmic dispiration in $(D+1)$ -dimensional spacetime

This paper investigates the vacuum-induced current density of a charged scalar field in a $(D+1)$ -dimensional cosmic dispiration spacetime threaded by a magnetic flux, demonstrating that the helical geometry of the defect generates both azimuthal and axial current components that are periodic in the magnetic flux and significantly influenced by the screw dislocation parameter.

Herondy Mota2026-04-10⚛️ hep-th

Integrals of motion in $WE_6$ CFT and the ODE/IM correspondence

This paper establishes the ODE/IM correspondence for the affine Lie algebra $E_6^{(1)}$ by demonstrating that the period integrals of the WKB expansion of the associated ordinary differential equation match the eigenvalues of the integrals of motion in the corresponding $WE_6$ conformal field theory up to the sixth order.

Daichi Ide, Katsushi Ito, Wataru Kono2026-04-10⚛️ hep-th

The Schwarz function and the shrinking of the Szeg\H{o} curve: electrostatic, hydrodynamic, and random matrix models

This paper investigates the deformation of the Szegő curve through electrostatic, hydrodynamic, and random matrix models, demonstrating that the curves' Schwarz functions are expressible via the Lambert $W$ function and that their $S$ -property corresponds to Schwarz reflection symmetry, all within the context of the asymptotic zero distribution of scaled Laguerre polynomials in a critical regime.

Gabriel Álvarez, Luis Martínez Alonso, Elena Medina2026-04-10🔢 math-ph

A unified 4D phase-space framework for two-level quantum dynamics: open-source library

This paper introduces a versatile, open-source numerical library that utilizes a 4D phase-space Wigner-Weyl formulation with a spectral splitting method to simulate the quantum dynamics of two-level particle gases across diverse fields ranging from nanomaterials to topological superconductors.

O. Morandi2026-04-10🔢 math-ph

Kohn--Nirenberg quantization of the affine group and related examples

This paper constructs unitary dual 2-cocycles and associated Kohn–Nirenberg quantizations for a class of semidirect product groups, including the affine group and Lie groups with Frobenius seaweed Lie algebras, by leveraging their double crossed product structure and a scalar Fourier transform that intertwines regular representations with dressing transformations.

Pierre Bieliavsky, Victor Gayral, Sergey Neshveyev, Lars Tuset2026-04-10🔢 math-ph

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