On Mathieu moonshine and Gromov-Witten invariants
Andreas Banlaki (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria); Abhishek Chowdhury (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria, IIT Bhubaneshwar, SBS Building, Argul, Khordha, Odisha, 752050, India); Abhiram Kidambi (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria); Maria Schimpf (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria)
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.
