Non Abelian Bosonization in Two and Three Dimensions

Abstract We discuss non-abelian bosonization of two- and three-dimensional fermions using a pathintegral framework in which the bosonic action follows from the evaluation of the fermion determinant for the Dirac operator in the presence of a vector field. This naturally leads to the Wess-Zumino-Witten action for massless two-dimensional fermions and to a Chem-Simons action for very massive three-dimensional fermions. One advantage of our approach is that it allows one to derive the exact bosonization recipe for fermion currents in a systematic way.