Three Avatars of Mock Modularity

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.

36 pages. Lectures delivered at 2020 ICTP Online Summer School on String Theory and Related Topics. Based on arXiv:1208.4074, arXiv:1905.05207, arXiv:2004.14387

References in corpus (4)

• Mock Theta Functions
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Lectures on Quantum Black Holes
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models