The non-compact elliptic genus: mock or modular

Understand

We analyze various perspectives on the elliptic genus of non-compact supersymmetric coset conformal field theories with central charge larger than three.

• We calculate the holomorphic part of the elliptic genus via a free field description of the model, and show that it agrees with algebraic expectations.
• The holomorphic part of the elliptic genus is directly related to an Appell-Lerch sum and behaves anomalously under modular transformation properties.
• We analyze the origin of the anomaly by calculating the elliptic genus through a path integral in a coset conformal field theory.