@article{58a8fb744733412ba612504cfd216c29,
title = "Characters of topological N = 2 vertex algebras are Jacobi forms on the moduli space of elliptic supercurves",
abstract = "We show that trace functions on modules of topological N=2 super vertex algebras give rise to conformal blocks on elliptic supercurves. We show that they satisfy a system of linear partial differential equations with respect to the modular parameters of the supercurves. Under some finiteness condition on the vertex algebra these differential equations can be interpreted as a connection on the vector bundle of conformal blocks. We show that this connection is equivariant with respect to a natural action of the Jacobi modular group on the modular parameters and the trace functions. In the appendix we prove the convergence of the trace functions.",
keywords = "Chiral algebras, Elliptic curves, Jacobi forms, Modular invariance, Supercurves, Vertex algebras",
author = "R. Heluani and {Van Ekeren}, J.",
note = "Funding Information: Acknowledgments: JVE would like to thank IMPA, where he was a postdoc while the bulk of this work was carried out, as well as the IH{\'E}S and the Alexander von Humboldt Foundation for financial support. RH would like to thank Nathan Berkovits for illuminating discussions and the explanation in 6.18 . He would also like to thank Yongchang Zhu for providing a printed copy of his Yale Ph.D. thesis. It goes without saying that this work borrows heavily from Zhu's seminal article. Both authors would like to thank Matt Krauel for kindly pointing out about some upcoming changes in the preprint [23] , this prompted the addition of the appendix in this manuscript. Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",
year = "2016",
month = oct,
day = "22",
doi = "10.1016/j.aim.2016.05.018",
language = "English (US)",
volume = "302",
pages = "551--627",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}