English

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-NN asymptotic expansion of the (central) trace of the heat kernel on any compact classical group GNGLN(C)G_N\subset\mathrm{GL}_N(\mathbb{C}), which extends a previous result known only for U(N)\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.

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}
}
R2 v1 2026-07-01T07:32:12.174Z