QED_2 and U(1)-Problem

TL;DR

This paper constructs and analyzes the massive N-flavor QED_2 using Euclidean path integrals, exploring its vacuum structure, bosonization, and the U(1)-problem, with results on mass spectra and confinement.

Contribution

It introduces a perturbative approach to massive QED_2 with N flavors, compares its vacuum structure to QCD, and solves the U(1)-problem within this model.

Findings

Proves convergence of mass perturbation series with finite cutoff

Identifies the sector generated by conserved vector currents

Shows a Witten-Veneziano formula for pseudoscalar mass spectrum

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.