Non-Compact SCFT 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]].