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arXiv · 1811.11619

On Mathieu moonshine and Gromov-Witten invariants

Andreas Banlaki·Abhishek Chowdhury·Abhiram Kidambi·Maria Schimpf
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Abstract

We show that a large number of $CY_3$ 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 $CY_3$ 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.

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Andreas Banlaki, Abhishek Chowdhury, Abhiram Kidambi, Maria Schimpf. 2018-11-28. On Mathieu moonshine and Gromov-Witten invariants. https://doi.org/10.1007/jhep02(2020)082

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