Conformal characters and the modular representation

TL;DR

This paper introduces a method to derive characters of all rational conformal field theories from any given modular group representation, demonstrated through the Yang-Lee and Ising models.

Contribution

It provides a general procedure to determine conformal characters from modular group representations, applicable to various rational conformal field theories.

Findings

Successfully applied to Yang-Lee and Ising models

Provides a systematic way to find all characters for a given modular representation

Enhances understanding of the link between modular representations and conformal field theories

Abstract

A general procedure is presented to determine, given any suitable representation of the modular group, the characters of all possible Rational Conformal Field Theories whose associated modular representation is the given one. The relevant ideas and methods are illustrated on two non-trivial examples: the Yang-Lee and the Ising models.