%0 Generic %1 troost2010noncompact %A Troost, Jan %D 2010 %K compact elliptic genus mock modular %T The non-compact elliptic genus: mock or modular %U http://arxiv.org/abs/1004.3649 %X 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. The path integral codes both the holomorphic part of the elliptic genus, and a non-holomorphic remainder that finds its origin in the continuous spectrum of the non-compact model. The remainder term can be shown to agree with a function that mathematicians introduced to parameterize the difference between mock theta functions and Jacobi forms. The holomorphic part of the elliptic genus thus has a path integral completion which renders it non-holomorphic and modular.

@misc{troost2010noncompact, abstract = {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. The path integral codes both the holomorphic part of the elliptic genus, and a non-holomorphic remainder that finds its origin in the continuous spectrum of the non-compact model. The remainder term can be shown to agree with a function that mathematicians introduced to parameterize the difference between mock theta functions and Jacobi forms. The holomorphic part of the elliptic genus thus has a path integral completion which renders it non-holomorphic and modular.}, added-at = {2013-12-23T06:54:33.000+0100}, author = {Troost, Jan}, biburl = {https://www.bibsonomy.org/bibtex/293067068c1a0ec7b3e40d453283cf379/aeu_research}, description = {The non-compact elliptic genus: mock or modular}, interhash = {1d6c42642da3611d45f06baebb0a30fe}, intrahash = {93067068c1a0ec7b3e40d453283cf379}, keywords = {compact elliptic genus mock modular}, note = {cite arxiv:1004.3649Comment: 13 pages}, timestamp = {2013-12-23T06:54:33.000+0100}, title = {The non-compact elliptic genus: mock or modular}, url = {http://arxiv.org/abs/1004.3649}, year = 2010 }