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.

🔢 mathematics

Localized Generative Design of Ship Hulls with Diffusion Models and High-Fidelity Assessment

This paper presents a reward-directed diffusion framework for localized ship hull optimization but demonstrates through high-fidelity CFD validation that current surrogate-based screening and reward formulations can miss critical performance trade-offs and fail to capture complex geometric features like faired bulbous bows, highlighting the necessity of integrating detailed physical assessments to refine generative design objectives.

Hadi Keramati, Mohammed A. Hannan, Patrick Kirchen, Sina Tousi, Joonas Riekkinen, Jim Pyra, Rajeev K. Jaiman2026-10-12

🔢 mathematics

Finiteness of planar central configurations of five bodies for all positive masses

This paper resolves Smale's sixth problem for the planar five-body problem by proving that for any choice of five positive masses, there are only finitely many central configurations up to similarity, utilizing a combination of algebraic valuation analysis, potential expansion near singular clusters, and computer-assisted exact rational certificates.

Tejasvi Singh Tomar2026-10-12

🔢 mathematics

BKT transition for $\mathsf{Sine}_\beta$

The paper proves the existence of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the large-distance behavior of the two-point correlation function for the $\mathsf{Sine}_\beta$ point process across all $\beta>0$ , thereby confirming a key asymptotic prediction made by Forrester.

Theodoros Assiotis2026-10-12

🔢 mathematics

A discrete analogue of $\mathscr{N}=2$ super Weil-Petersson volumes

This paper introduces a discrete spectral curve derived from $\mathscr{N}=2$ double-scaled SYK that generates quasi-polynomial volumes via topological recursion, which recover Turiaci and Witten's super Weil-Petersson volumes in the continuum limit and admit an all-genus intersection-theoretic interpretation on the moduli space of stable marked curves.

Wasif Ahmed, Joydeep Naskar2026-10-12

🔢 mathematics

TAP variational formula for 2-spin models with general interaction matrix and marginality

This paper establishes a Thouless-Anderson-Palmer (TAP) variational formula for the free energy of spherical 2-spin models with general interaction matrices at all temperatures by introducing a novel microcanonical proof that partitions the state space to separate macroscopic low-temperature contributions from high-temperature fluctuations, thereby resolving the challenges posed by marginality.

David Belius, Simon Briend, Volodymyr Fomichov2026-10-12

🔢 mathematics

Modular Properties of Generalised Gibbs Ensembles: The Deformed KdV Hierarchy

This paper constructs and analyzes a set of deformed quantum KdV charges associated with modular transformations of Generalised Gibbs Ensembles, proving their commutativity and uniqueness while demonstrating that their eigenvalues in free fermion and Lee-Yang models align with Thermodynamic Bethe Ansatz predictions.

Faisal Karimi2026-10-12

🔢 mathematics

Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets

This paper mathematically proves the existence of energy-minimizing Hopfions in a continuum model of frustrated magnets with competing exchange interactions and an external field, while also characterizing the strong-field asymptotic behavior and convergence of these configurations.

Glal Bacho, Christof Melcher2026-10-12

🔢 mathematics

Unifying spherical convolutions through lifting

This paper presents a unified framework for spherical convolutions by lifting spin fields to the rotation group $\text{SO(3)}$ , thereby reconciling existing definitions, establishing theoretical limits on equivariance, and providing efficient harmonic-space algorithms implemented in the open-source s2conv code.

J. D. McEwen2026-10-12

🔢 mathematics

Modularity in $d > 2$ free conformal field theory

This paper derives new closed-form expressions for the partition functions of free conformally-coupled scalars in even dimensions by identifying them with multiple elliptic Gamma functions, whose modular properties are utilized to resum high-temperature expansions and provide a geometric interpretation within superconformal field theory.

Yang Lei, Sam van Leuven2026-10-09

🔢 mathematics

Verlinde rings and cluster algebras arising from quantum affine algebras

This paper formulates and proves a positivity conjecture linking the Verlinde ring of untwisted affine Lie algebras to a subcategory of quantum affine algebra representations via a ring homomorphism, leveraging connections to finite-type cluster algebras to establish the result for simply-laced types at level 2 and type $A_1$ at arbitrary levels.

Chul-hee Lee, Jian-Rong Li, Euiyong Park2026-10-09

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math-ph

Localized Generative Design of Ship Hulls with Diffusion Models and High-Fidelity Assessment

Finiteness of planar central configurations of five bodies for all positive masses

BKT transition for Sineβ\mathsf{Sine}_\betaSineβ​

A discrete analogue of N=2\mathscr{N}=2N=2 super Weil-Petersson volumes

TAP variational formula for 2-spin models with general interaction matrix and marginality

Modular Properties of Generalised Gibbs Ensembles: The Deformed KdV Hierarchy

Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets

Unifying spherical convolutions through lifting

Modularity in d>2d > 2d>2 free conformal field theory

Verlinde rings and cluster algebras arising from quantum affine algebras

BKT transition for $\mathsf{Sine}_\beta$

A discrete analogue of $\mathscr{N}=2$ super Weil-Petersson volumes

Modularity in $d > 2$ free conformal field theory