On Mathieu moonshine and Gromov-Witten invariants

Abstract

We provide further evidence that CY3 manifolds are involved in an intricate way in Mathieu moonshine, i.e., 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 � T2 and type IIA string theory on CY3 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. � 2020, The Author(s).