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.

arXiv comment28 pages + appendices; v2: publication version

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• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• On a ${\mathbb{Z}}_3$-valued discrete topological term in 10d heterotic string theories
• A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms
• 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