One-point theta functions for vertex operator algebras

TL;DR

This paper introduces and analyzes one-point theta functions for VOA modules, generalizing classical character functions and establishing their transformation properties under modular group actions.

Contribution

It defines a new class of one-point theta functions for VOAs and proves their modular transformation laws, extending previous character theory.

Findings

Established transformation laws under SL_2(Z)

Generalized classical character theta functions

Provided foundational properties for VOA modules

Abstract

One-point theta functions for modules of vertex operator algebras (VOAs) are defined and studied. These functions are a generalization of the character theta functions studied by Miyamoto and are deviations of the classical one-point functions for modules of a VOA. Transformation laws with respect to the group $\operatorname{SL}_2(\mathbb{Z})$ are established.