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 language | English (US) |
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Pages (from-to) | 551-627 |
Number of pages | 77 |
Journal | Advances in Mathematics |
Volume | 302 |
DOIs | |
State | Published - Oct 22 2016 |
Keywords
- Chiral algebras
- Elliptic curves
- Jacobi forms
- Modular invariance
- Supercurves
- Vertex algebras
ASJC Scopus subject areas
- General Mathematics