Topological modularity of Supermoonshine

Abstract

The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory's gravitational anomaly. In this note we verify this prediction in Duncan's Supermoonshine module, as well as in tensor products and orbifolds thereof. Along the way we develop machinery for computing the elliptic genera of general alternating orbifolds and discuss the relation of this construction to the elusive "periodicity class" of TMF.

28 pages + appendices; v2: publication version

References in corpus (4)

• Notes on the K3 Surface and the Mathieu group M_24
• Permutation orbifolds and holography
• Undoing decomposition
• BPS Algebras in 2D String Theory

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• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results