Vertex operator algebras and weak Jacobi forms

Details Vertex operator algebras and weak Jacobi forms Vertex operator algebras and weak Jacobi forms

2011-03-04

arxiv.org/abs/1103.0994v1

Mathematics

Quantum Algebra

Scientific paper

Let $V$ be a strongly regular vertex operator algebra. For a state $h \in V_1$ satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr$_Mq^{L(0)-c/24}\zeta^{h(0)} ($M$ a $V$-module) is a vector-valued weak Jacobi form of weight 0 and a certain index $/2$. We discuss refinements and applications of this result when $V$ is holomorphic, in particular we prove that if $g = e^{h(0)}$ is a finite order automorphism then Tr$_V q^{L(0)-c/24}g$ is a modular function of weight 0 on a congruence subgroup of $SL_2(Z)$.

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