  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]].
