The central heat trace on large compact classical groups

TL;DR

This paper derives the large-N asymptotic expansion of the central heat kernel trace on all compact classical groups, revealing new geometric and string theory interpretations and dualities in two-dimensional gauge theories.

Contribution

It extends previous results from U(N) to all compact classical groups and introduces new geometric and string dualities related to the heat kernel trace.

Findings

Asymptotic expansion of heat kernel trace for all classical groups

Connections to ramified coverings and Gromov-Witten invariants

Exploration of gauge/string dualities in two dimensions

Abstract

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.