Three Avatars of Mock Modularity

TL;DR

This paper explores three different physical contexts—holography, topology, and duality—where mock modularity, originating from Ramanujan's mock theta functions, plays a significant role in modern mathematical physics.

Contribution

It provides a comprehensive overview of how mock modularity manifests in three key areas of physics, connecting historical mathematical concepts with contemporary physical theories.

Findings

Mock modularity appears in holography, topology, and duality.

It offers new insights into the mathematical structures underlying physical theories.

The paper bridges historical mathematics with modern physics applications.

Abstract

Mock theta functions were introduced by Ramanujan in 1920 but a proper understanding of mock modularity has emerged only recently with the work of Zwegers in 2002. In these lectures we describe three manifestations of this apparently exotic mathematics in three important physical contexts of holography, topology and duality where mock modularity has come to play an important role.