Topological modularity of Supermoonshine

TL;DR

This paper verifies a prediction of topological modular forms regarding elliptic genera in Duncan's Supermoonshine module and related constructions, developing new computational tools and exploring their theoretical implications.

Contribution

It introduces methods for computing elliptic genera of orbifolds and connects these results to the periodicity class in TMF, advancing understanding of topological modularity in superconformal theories.

Findings

Verified divisibility property of elliptic genera in Supermoonshine

Developed machinery for orbifold elliptic genus computations

Explored relation to TMF periodicity class

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.