# zbMATH — the first resource for mathematics

On Mathieu moonshine and Gromov-Witten invariants. (English) Zbl 1435.83164
Summary: 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 $$K3 \times T^2$$ 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.

##### MSC:
 83E30 String and superstring theories in gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14J28 $$K3$$ surfaces and Enriques surfaces 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 32Q25 Calabi-Yau theory (complex-analytic aspects)
PALP; TOPCOM
Full Text: