QED_2 and U(1)-Problem

Abstract

QED_2 with mass and N flavors of fermions is constructed using Euclidean path integrals. The fermion masses are treated perturbatively and the convergence of the mass perturbation series is proven for a finite space-time cutoff. The expectation functional is decomposed into clustering theta-vacua and their properties are compared to the theta-vacua of QCD for zero fermion mass. The sector that is created by the N^2 classically conserved vector currents is identified. The currents that correspond to a Cartan subalgebra of U(N) are bosonized together with the chiral densities in terms of a generalized Sine-Gordon model. The solution of the U(1)-problem of QED_2 is discussed and a Witten-Veneziano formula is shown to hold for the mass spectrum of the pseudoscalars. Evaluation of the Fredenhagen-Marcu confinement order parameter clarifies the structure of superselection sectors.