A modular invariance property of multivariable trace functions for regular vertex operator algebras

Abstract

We prove an ${\text{SL}}_2(\mathbb{Z})$-invariance property of multivariable trace functions on modules for a regular VOA. Applying this result, we provide a proof of the inversion transformation formula for Siegel theta series. As another application, we show that if $V$ is a regular VOA containing a regular subVOA $U$ whose commutant $U^c$ is regular and satisfies $(U^c{)}^c=U$, then all simple $U$-modules appear in some simple $V$-module.

18 pages, additional references added, typos corrected, and some additional information included

References in corpus (2)

• Modular invariance of trace functions in orbifold theory
• Intertwining operators and modular invariance

Cited by in corpus (1)

• Schur-Weyl Duality for Heisenberg Cosets