Mock modularity and a secondary elliptic genus

TL;DR

This paper explores refined deformation invariants in supersymmetric field theories suggested by Topological Modular Forms, introducing mock modular forms to explain integrality properties of certain invariants.

Contribution

It provides a physical definition of refined invariants beyond the elliptic genus, connecting mock modular forms to these invariants.

Findings

Mock modular forms explain integrality of certain invariants.

Refined invariants are more sensitive than the standard elliptic genus.

Physical interpretation of these invariants is established.

Abstract

The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of some of these invariants. The theory of mock modular forms makes a surprise appearance, shedding light on the integrality properties of some well-known examples.