Mathieu Moonshine and N=2 String Compactifications

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 \times 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 F_n.

28 pages; v2: minor changes, published version

References in corpus (4)

• Notes on the K3 Surface and the Mathieu group M_24
• Note on Twisted Elliptic Genus of K3 Surface
• Mathieu Moonshine in the elliptic genus of K3
• Polynomial Structure of the (Open) Topological String Partition Function

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• Dyon degeneracies from Mathieu moonshine
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• Mathieu moonshine in four dimensional $\mathcal{N}=1$ theories
• Eta Products, BPS States and K3 Surfaces
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Dressed elliptic genus of heterotic compactifications with torsion and general bundles
• New supersymmetric index of heterotic compactifications with torsion
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• On Mathieu moonshine and Gromov-Witten invariants
• Calabi-Yau manifolds and sporadic groups
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines