A Unified Scheme for Modular Invariant Partition Functions of WZW Models

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.