Anomalous non-Abelian gauge theory in two dimensions

Abstract

We consider the two-dimensional model of a U(N) gauge field coupled to just the right-handed current of N massless fermions. We show, using its bosonized version, that this model, although anomalous and non-gauge invariant, formally yields a consistent unitary Lorentz-invariant quantum theory. As by-products, the commutators of the currents and to the Gauss-law generators are obtained explicitly.