On Mathieu moonshine and Gromov-Witten invariants

Abstract

We show that a large number of $C{Y}_3$ manifolds are involved in an intricate way in Mathieu moonshine viz. their Gromov--Witten invariants are related to the expansion coefficients of the twined/ twisted--twined elliptic genera of $K3$. We use the string duality between CHL orbifolds of heterotic string theory on $K3\times T^2$ and type IIA string theory on $C{Y}_3$ manifolds to explicitly show this connection. We then work out two concrete examples where we exactly match the expansion coefficients on both sides of the duality.

28 pages, 2 tables, appendices taken from arXiv:1711.09698. V2: Corrected typos, added references