A Unified Scheme for Modular Invariant Partition Functions of WZW Models

TL;DR

This paper presents a unified method for systematically constructing modular invariant partition functions for WZW models at any level, by modding out known theories with discrete groups, and applies it to several Lie groups.

Contribution

It introduces a general approach to find all modular invariant partition functions for WZW models, including new solutions, applicable to various Lie groups.

Findings

Recovered all known partition functions for the studied models.

Discovered new modular invariant partition functions.

Provided explicit formulas for all obtained partition functions.

Abstract

We introuduce a unified method which can be applied to any WZW model at arbitrary level to search systematically for modular invariant physical partition functions. Our method is based essentially on modding out a known theory on group manifold $G$ by a discrete group $\Gamma$. We apply our method to $\widehat {su(n)}$ with $n=2,3,4,5,6$, and to $\widehat {g_2}$ models, and obtain all the known partition functions and some new ones, and give explicit expressions for all of them.