3307 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.
This paper introduces a novel optimization framework that jointly designs modular coils and vacuum vessels for stellarators, enabling the first realization of precise snowflake divertors alongside standard X-point and null configurations for next-generation prototypes.
The paper disproves Maxwell's conjecture by presenting a specific configuration of five point charges in Euclidean space that generates 24 non-degenerate critical points in its electrostatic potential, exceeding the conjectured maximum of .
This paper presents a comprehensive computational study of the mod-2 cohomology for all 230 three-dimensional space groups, providing explicit ring presentations and degree- cocycles to establish a framework for identifying Lieb-Schultz-Mattis anomaly candidates via Wyckoff positions and applying these constraints to U(1) quantum spin liquids on the 3D pyrochlore lattice.
This paper reviews the bootstrap approach to exactly solvable two-dimensional conformal field theories without extended chiral symmetry, demonstrating how local conformal symmetry and degenerate fields constrain spectra and correlation functions to yield analytic solutions for theories including Liouville, minimal models, and loop CFTs.
This paper establishes a systematic framework using (3+1)d Dijkgraaf-Witten Symmetry Topological Field Theories and generalized "club sandwich" interfaces to classify and construct gapless phases with non-invertible categorical symmetries, including intrinsically gapless SPTs and symmetry-breaking phases, by extending known phase transitions of smaller symmetries.
This paper constructs explicit Tachyon-Chern-Simons terms in the holographic V-QCD model for generic complex tachyon fields to ensure flavor anomaly consistency, demonstrating that baryon number equals the topological instanton number and that the resulting effective pion action reproduces the chiral Lagrangian with Skyrme and Wess-Zumino-Witten terms.
This paper derives blow-up equations to resum singular instanton expansions of Nekrasov--Shatashvili functions in four-dimensional gauge theories at resonant loci, thereby revealing the analytic structure of Heun functions and constructing finite periodic, antiperiodic, and logarithmic solutions that describe spectral gap edges and semisimple monodromy.
This paper introduces and proves that a specific family of quadratic invariants in Pauli expectation values constitutes a state-independent characterization of pure n-qubit states, generalizing previously known two-qubit "pentagon identities" to arbitrary system sizes through novel structural insights into complementarity and mutual unbiasedness.
This paper establishes that observables associated with the n-qubit Pauli group, including degenerate ones, exhibit maximal complementarity by deriving criteria for their compatibility, linking maximal sets to informational pure state complementarity equalities and mutually unbiased bases, and demonstrating that these sets entail strong entropic uncertainty relations.
This paper proposes an efficient strong-form phase-field solver that integrates the Gradient Smoothing Method with a hierarchical adaptive moving mesh to achieve near-linear computational scaling and high accuracy for large-scale interface evolution problems by localizing fine resolution to narrow interfacial regions while maintaining coarse discretization in bulk domains.