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.

Euler transformation for multiple $q$ -hypergeometric series from wall-crossing formula of $K$ -theoretic vortex partition function

This paper establishes that transformation formulas for multiple $q$ -hypergeometric series, specifically the Kajihara and Hallnäs–Langmann–Noumi–Rosengren transformations, correspond to wall-crossing formulas of $K$ -theoretic vortex partition functions in 3d $\mathcal{N}=2$ and $\mathcal{N}=4$ gauge theories, thereby providing a geometric interpretation of these Euler transformations via the wall-crossing behavior of handsaw quiver varieties.

Yutaka Yoshida2026-04-03🔢 math-ph

Quantum inverse scattering for the 20-vertex model up to Dynkin automorphism: 3D Poisson structure, triangular height functions, weak integrability

This paper initiates a novel application of the quantum inverse scattering method to the 20-vertex model by utilizing higher-dimensional L-operators to establish a 3D Poisson structure, triangular height functions, and a framework for weak integrability, thereby extending the study of Hamiltonian systems beyond the previously analyzed 6-vertex model.

Pete Rigas2026-04-03🔢 math-ph

Existence of higher degree minimizers in the magnetic skyrmion problem

This paper proves the existence of topologically nontrivial energy-minimizing maps with higher degrees in a magnetic skyrmion model by strategically inserting truncated Belavin-Polyakov profiles into lower-degree configurations, provided the domain is sufficiently large or slender to prevent degree loss.

Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov2026-04-03🔬 cond-mat.mes-hall

Skyrmion stacking in stray field-coupled ultrathin ferromagnetic multilayers

This paper derives a reduced energy functional for ultrathin ferromagnetic multilayers hosting skyrmions and demonstrates that in bilayer systems, the global energy minimizers consist of two antiparallel Néel skyrmions stabilized by stray field coupling.

N. J. Dubicki, V. V. Slastikov, A. Bernand-Mantel, C. B. Muratov2026-04-03🌀 nlin

Explicit construction of states in orbifolds of products of $N=2$ Superconformal ADE Minimal models

This paper generalizes the explicit construction of orbifold states in products of $N=(2,2)$ minimal models to include D and E-type modular invariants, demonstrating that spectral flow twisting is consistent with nondiagonal pairings and that the resulting mirror isomorphism between dual group orbifolds is inherently built into the construction, as illustrated by the $\textbf{A}_{2}\textbf{E}_7^{3}$ model.

Boris Eremin, Sergej Parkhomenko2026-04-03⚛️ hep-th

Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity

This paper reinterprets the Hamilton-Jacobi equation as a model reduction that eliminates velocity degrees of freedom, thereby extending its applicability to general Newtonian systems with non-conservative forces and deriving a dissipative Schrödinger equation through a geometric optics approximation.

Amit Acharya2026-04-03✓ Author reviewed ⓘ🔢 math-ph

Approximating the Permanent of a Random Matrix with Polynomially Small Mean: Zeros and Universality

This paper demonstrates that for random matrices with standard complex Gaussian entries, the zeros of the permanent polynomial $\mathrm{per}(zJ + W)$ are confined to a disk of radius $\tilde{O}(n^{-1/3})$ , thereby enabling efficient approximation algorithms for the permanent with polynomially small biases while simultaneously proving that the bulk of these zeros lie at magnitude $\Theta(n^{-1/2})$ to preserve the conjectured average-case hardness of the problem.

Frederic Koehler, Pui Kuen Leung2026-04-03🔢 math-ph

Hierarchical symmetry selects log-Poisson cascades: classification, uniqueness, and stability

This paper demonstrates that hierarchical symmetry serves as a necessary and sufficient condition to uniquely select log-Poisson cascades from the broader log-infinitely-divisible family, while also establishing their classification and stability under approximate symmetry.

E. M. Freeburg2026-04-03🔢 math-ph

One-Parameter Family of Elliptic Sine-Gordon Equations

This paper introduces and analyzes a continuous one-parameter family of elliptic sine-Gordon equations characterized by the modulus of Jacobi elliptic functions, which interpolates between the integrable sine-Gordon and sine-hyperbolic-Gordon equations in the limits of zero and one, respectively, and derives their kink solutions for various modulus values.

Avinash Khare, Avadh Saxena2026-04-03🌀 nlin

Equivalence of toral Chern-Simons and Reshetikhin-Turaev theories

This paper establishes a natural isomorphism between toral Chern-Simons theory with gauge group $\mathbb{T} \cong U(1)^n$ and the Reshetikhin-Turaev theory associated with the pointed modular category of the discriminant group of an even, integral, nondegenerate symmetric bilinear form, proving their equivalence as extended $(2+1)$ -dimensional TQFTs for both closed 3-manifolds and bordisms with boundary.

Daniel Galviz2026-04-03🔢 math-ph

← Previous Next →

math-ph

Euler transformation for multiple qqq-hypergeometric series from wall-crossing formula of KKK-theoretic vortex partition function