The central heat trace on large compact classical groups

Fuente: arXiv
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Main Authors: Lemoine, Thibaut, Maïda, Mylène
Format: Preprint
Published: 2025
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author Lemoine, Thibaut
Maïda, Mylène
author_facet Lemoine, Thibaut
Maïda, Mylène
contents We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It admits two new interpretations of the trace: in terms of ramified coverings of the torus, and Gromov-Witten invariants on elliptic curves. These connections allow us to explore several aspects of the gauge/string duality in two dimensions: a Yang-Mills/Hurwitz duality, and Yang-Mills/Gromov-Witten duality.
format Preprint
id arxiv_https___arxiv_org_abs_2511_08288
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The central heat trace on large compact classical groups
Lemoine, Thibaut
Maïda, Mylène
Mathematical Physics
Algebraic Geometry
Combinatorics
Probability
Spectral Theory
05A17, 14H30, 43A75, 58J50 (primary), 81T13, 81T35 (secondary)
We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It admits two new interpretations of the trace: in terms of ramified coverings of the torus, and Gromov-Witten invariants on elliptic curves. These connections allow us to explore several aspects of the gauge/string duality in two dimensions: a Yang-Mills/Hurwitz duality, and Yang-Mills/Gromov-Witten duality.
title The central heat trace on large compact classical groups
topic Mathematical Physics
Algebraic Geometry
Combinatorics
Probability
Spectral Theory
05A17, 14H30, 43A75, 58J50 (primary), 81T13, 81T35 (secondary)
url https://arxiv.org/abs/2511.08288