Modular differential equations for characters of RCFT

TL;DR

This paper develops methods using vector-valued modular forms to find modular differential equations for RCFT characters, linking these equations to null vector relations in the operator algebra, with an example demonstration.

Contribution

It introduces algorithmic procedures to determine modular differential equations for RCFT characters based on vector-valued modular forms.

Findings

Derived modular differential equations for specific RCFT characters

Established a connection between these equations and null vector relations

Provided an explicit example illustrating the methods

Abstract

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.