🔢 Category

math-ph

3383 papers

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

Adiabatic Solutions of the Haydys-Witten Equations and Symplectic Khovanov Homology

This paper proposes a novel approach to proving Witten's conjecture on the isomorphism between instanton Floer homology and Khovanov homology by demonstrating that adiabatic solutions of decoupled Haydys-Witten equations correspond to non-vertical paths in a moduli space of extended Bogomolny equations, which can be modeled by the Grothendieck-Springer resolution and suggests a deep connection to symplectic Khovanov homology.

Michael Bleher2026-02-03
⚛️ lattice

On the moduli space of multi-fractional instantons on the twisted T4\mathbb T^4

This paper investigates the moduli space of multi-fractional instantons on a twisted T4\mathbb{T}^4 by demonstrating that 't Hooft's constant field strength solutions constitute the entire moduli space only when gcd⁡(k,r)=r\gcd(k,r)=r, whereas for gcd⁡(k,r)≠r\gcd(k,r)\neq r, they represent a measure-zero subset surrounded by non-constant, non-abelian solutions, a finding that resolves a recent puzzle and is validated through analytical, numerical, and lattice comparisons.

Mohamed M. Anber, Andrew A. Cox, Erich Poppitz2026-02-03
🔢 mathematics

Retraction Dynamics of a Highly Viscous Liquid Sheet

This paper investigates the capillary-driven retraction of a highly viscous liquid sheet in the limit of large Ohnesorge and aspect ratios, deriving a reduced heat-equation model with a single dimensionless parameter that reveals distinct retraction regimes—including early-time growth, a Taylor-Culick intermediate phase for long sheets, and late-time decay—through asymptotic matching of thin-film and tip-flow dynamics.

Taosif Ahsan, Rodolfo Brandão, Benny Davidovitch, Howard A. Stone2026-02-03
🔢 mathematics

Higher-order transformations of bidirectional quantum processes

This paper characterizes the most general forms of input-output indefiniteness in bidirectional quantum devices by establishing a hierarchy of higher-order transformations built from bistochastic channels, which encompasses both indefinite local directions and indefinite global causal orders within a time-symmetric quantum framework.

Luca Apadula, Alessandro Bisio, Giulio Chiribella, Paolo Perinotti, Kyrylo Simonov2026-02-03