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

Finite- and long-range spin-wave free-energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet

This paper proves the leading low-temperature free energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet with power-law exchange interactions, establishing fractional and logarithmically corrected laws for long-range cases and extending Takahashi's quadratic law to kernels with finite second moments, with results supported by Quantum Monte Carlo simulations.

Andreas Klippel2026-10-09

🔢 mathematics

Polynomial and Eigenspace Factorisations for the One-loop Dilatation Operator at Finite $N$

This paper investigates the one-loop dilatation operator in the $su(2)$ sector of $\mathcal{N}=4$ super Yang-Mills theory at finite $N$ by establishing that its characteristic polynomial on the $U(N)$ state space divides the large- $N$ limit, demonstrating an eigenspace factorisation into infinite towers generated by $SU(N)$ eigenstates, and proposing a direct permutation framework for the $SU(N)$ spectral problem based on an intersection with derangements.

Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki2026-10-09

🔢 mathematics

The three- and four-loop equal-mass sunset integrals and local Calabi--Yau fourfolds and fivefolds

This paper establishes that the equal-mass three- and four-loop sunset Feynman integrals in two dimensions are explicitly determined by the genus-zero Gromov–Witten theory of local Calabi–Yau fourfolds and fivefolds, specifically relating the integrals to the one-point potential and its gravitational descendants rather than a prepotential.

Hartmut Maennel, Pierre Vanhove2026-10-09

🔢 mathematics

Equal-mass sunset integrals and genus-zero local Gromov--Witten theory of Calabi--Yau $n$ -folds

This paper establishes an exact identity linking equal-mass $(n-1)$ -loop sunset Feynman integrals to genus-zero one-point descendant invariants of local Calabi–Yau $n$ -folds, while also proving the global univalence of the principal mirror map and characterizing the associated evaluation divisors and constants.

Hartmut Maennel, Pierre Vanhove2026-10-09

🔢 mathematics

Quantum geometry at arbitrary genus - I: Anharmonic potentials

This paper resolves the long-standing open problem of establishing a non-perturbative P/NP relation for arbitrary-genus quantum potentials by utilizing complex algebraic geometry and exact WKB methods to overcome the symplectic group mismatch in higher genera, thereby deriving an all-orders quantum P/NP relation explicitly for genus-2 and genus-3 anharmonic oscillators.

Mustafa Türe, Mithat Ünsal2026-10-09

🔢 mathematics

Dirac operators on periodic planar graphs: the right definition advocated by flat bands

This paper investigates massive discrete Dirac-type operators on periodic planar graphs, demonstrating that neglecting faces yields spurious flat bands and establishing a spectral reduction that links the operator's spectrum to vertex and face Laplacians to correctly characterize flat bands on Archimedean and Lieb lattices.

Koichi Kato, Daniel Parra, Serge Richard2026-10-09

🔢 mathematics

Three-Point Trace Positivity:Schatten Norm Compression and Interpolating Metrics

This paper establishes the positivity of a specific three-point trace matrix for parameters $1/2 \le r \le 1$ , a result that simultaneously resolves the Lin–van den Driessche conjecture on Schatten norm compression and characterizes the exact range $t \in [1,2]$ for which a new family of interpolating metrics between Hellinger and Bures distances forms a complete metric on positive operators.

Trung Dung Vuong, Hiroyuki Osaka2026-10-09

🔢 mathematics

Uniformity theory of weighted composites

This paper proposes extending the mathematical framework of double groupoids to analyze spatially varying weighted composites, with the ultimate goal of classifying misalignment defects and their temporal evolution.

Marcelo Epstein, Mohammadjavad Javadi2026-10-09

🔢 mathematics

Quantum Gravity in Asymptotically Flat Spacetimes from Unstable D-Branes

This paper proposes a non-perturbative formulation of quantum gravity in asymptotically flat spacetimes by demonstrating that Witten's cubic open string field theory on unstable D-branes dynamically generates the closed string S-matrix through gauge-invariant operators, thereby establishing a concrete flat-space analogue of the AdS/CFT correspondence.

Roji Pius2026-10-09

🔢 mathematics

The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes

This paper establishes the Hawking and Penrose singularity theorems for Lorentz–Finsler structures with low $C^{(1,2)}$ or $C^{(1,3)}$ regularity by employing a two-stage approximation method that handles non-unique geodesics and distributional Ricci curvature, thereby extending previous $C^1$ Lorentzian results to the weighted Finsler setting.

Darius Erös, Ettore Minguzzi, Argam Ohanyan, Shin-ichi Ohta2026-10-09

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math-ph

Finite- and long-range spin-wave free-energy asymptotics for the two-dimensional quantum Heisenberg ferromagnet

Polynomial and Eigenspace Factorisations for the One-loop Dilatation Operator at Finite NNN

The three- and four-loop equal-mass sunset integrals and local Calabi--Yau fourfolds and fivefolds

Equal-mass sunset integrals and genus-zero local Gromov--Witten theory of Calabi--Yau nnn-folds

Quantum geometry at arbitrary genus - I: Anharmonic potentials

Dirac operators on periodic planar graphs: the right definition advocated by flat bands

Three-Point Trace Positivity:Schatten Norm Compression and Interpolating Metrics

Uniformity theory of weighted composites

Quantum Gravity in Asymptotically Flat Spacetimes from Unstable D-Branes

The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes

Polynomial and Eigenspace Factorisations for the One-loop Dilatation Operator at Finite $N$

Equal-mass sunset integrals and genus-zero local Gromov--Witten theory of Calabi--Yau $n$ -folds