Yang–Mills/Gromov–Witten duality in higher genus

Prove that the Yang–Mills/Gromov–Witten duality relating the large-N expansion of the Yang–Mills partition function for compact classical groups to Gromov–Witten invariants of an elliptic curve admits a generalization to arbitrary genera g≥2.

Background

The paper proves, for a two-dimensional torus, that the asymptotic coefficients of the central heat trace—and equivalently the genus-one Yang–Mills partition function—can be expressed through functionals of the generating function of Gromov–Witten invariants of an elliptic curve.

The authors state that extending this correspondence to higher-genus surfaces is conjectural. They note that such an extension would involve not only the heat-trace expansion but also the asymptotic expansion of the Witten zeta function, for which the cited literature provides only partial results.

References

We conjecture that it admits a generalization to any genus $g 2$; however, it is no longer only related to the expansion of the trace of the heat kernel, but also on the expansion of the Witten zeta function $\zeta_{G_N}$ , for which only two partial results have been obtained:

— The central heat trace on large compact classical groups  (2511.08288 - Lemoine et al., 11 Nov 2025) in Section “Applications to gauge/string duality,” subsection “Yang–Mills/Gromov–Witten duality”