Nonabelian parafermions and their dimensions

Abstract

We propose a generalization of the Zamolodchikov-Fateev parafermions which are abelian, to nonabelian groups. The fusion rules are given by the tensor product of representations of the group. Using Vafa equations we get the allowed dimensions of the parafermions. We find for simple groups that the dimensions are integers. For cover groups of simple groups, we find, for $n.G.m$, that the dimensions are the same as $Z_n$ parafermions. Examples of integral parafermionic systems are studied in detail.