The central heat trace on large compact classical groups
Mathematical Physics
2025-11-12 v1 Algebraic Geometry
Combinatorics
math.MP
Probability
Spectral Theory
Abstract
We establish the large- asymptotic expansion of the (central) trace of the heat kernel on any compact classical group , which extends a previous result known only for \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.
Cite
@article{arxiv.2511.08288,
title = {The central heat trace on large compact classical groups},
author = {Thibaut Lemoine and Mylène Maïda},
journal= {arXiv preprint arXiv:2511.08288},
year = {2025}
}