On Mathieu moonshine and Gromov-Witten invariants

Abstract

We show that a large number of $C{Y}_3$ 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 $C{Y}_3$ 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.

arXiv comment28 pages, 2 tables, appendices taken from arXiv:1711.09698. V2: Corrected typos, added references

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Cited by in corpus (3)

• Topological modularity of Supermoonshine
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines