On Mathieu moonshine and Gromov-Witten invariants

Abstract

Abstract We provide further evidence that CY 3 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 × T 2 and type IIA string theory on CY 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.

Keywords

• String Duality
• Superstrings and Heterotic Strings
• Differential and Algebraic Geometry
• Discrete Symmetries