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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)
Software:
PALP; TOPCOM
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