Non-Compact SCFT and Mock Modular Forms

TL;DR

This paper reviews research on the anomalous modular transformation properties in non-compact superconformal field theories, highlighting their connection to mock modular forms and summarizing collaborative studies on this mathematical-physical interplay.

Contribution

It synthesizes previous work on the modular properties of non-compact SCFTs, emphasizing the role of mock modular forms and providing insights into their mathematical structure.

Findings

Identification of mock modularity in non-compact SCFTs

Clarification of anomalous modular transformation properties

Connection between superconformal models and mock modular forms

Abstract

One of interesting issues in two-dimensional superconformal field theories is the existence of anomalous modular transformation properties appearing in some non-compact superconformal models, corresponding to the `mock modularity' in mathematical literature. I review a series of my studies on this issue in collaboration with T. Eguchi, mainly focusing on the papers [arXiv:1012.5721 [hep-th]], [arXiv:1407.7721 [hep-th]], [arXiv:1603.02903 [hep-th]].