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.