Discussing the U(1)-Problem of QED_2 without Instantons

TL;DR

This paper explores the U(1)-problem in two-dimensional QED with mass and flavor, using bosonization and symmetry analysis to derive a Witten-Veneziano-type formula for pseudoscalar masses.

Contribution

It introduces a detailed construction of QED_2 with additional terms and analyzes its vacuum structure without relying on instantons, connecting it to a generalized Sine-Gordon model.

Findings

Derived a Witten-Veneziano-type formula for pseudoscalar masses.

Compared vacuum properties to the theta-vacuum of QCD.

Established symmetry properties of the GSG model related to QED_2 vacuum.

Abstract

We construct QED_2 with mass and flavor and an extra Thirring term. The vacuum expectation values are carefully decomposed into clustering states using the U(1)-axial symmetry of the considered operators and a limiting procedure. The properties of the emerging expectation functional are compared to the proposed theta-vacuum of QCD. The massive theory is bosonized to a generalized Sine-Gordon model (GSG). The structure of the vacuum of QED_2 manifests itself in symmetry properties of the GSG. We study the U(1)-problem and derive a Witten-Veneziano-type formula for the masses of the pseudoscalars determined from a semiclassical approximation.