Abstract
There is a ‘Mathieu moonshine’ relating the elliptic genus of K3 to the sporadic group M 24. Here, we give evidence that this moonshine extends to part of the web of dualities connecting heterotic strings compactified on K3 × T 2 to type IIA strings compactified on Calabi-Yau threefolds. We demonstrate that dimensions of M 24 representations govern the new supersymmetric index of the heterotic compactifications, and appear in the Gromov-Witten invariants of the dual Calabi-Yau threefolds, which are elliptic fibrations over the Hirzebruch surfaces \( {{\mathbb{F}}_n} \).
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Cheng, M.C.N., Dong, X., Duncan, J.F.R. et al. Mathieu moonshine and \( \mathcal{N}=2 \) string compactifications. J. High Energ. Phys. 2013, 30 (2013). https://doi.org/10.1007/JHEP09(2013)030
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DOI: https://doi.org/10.1007/JHEP09(2013)030