Characters of topological N = 2 vertex algebras are Jacobi forms on the moduli space of elliptic supercurves

R. Heluani*, J. Van Ekeren

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)551-627
Number of pages77
JournalAdvances in Mathematics
Volume302
DOIs
StatePublished - Oct 22 2016

Keywords

  • Chiral algebras
  • Elliptic curves
  • Jacobi forms
  • Modular invariance
  • Supercurves
  • Vertex algebras

ASJC Scopus subject areas

  • Mathematics(all)

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