The phases of two-dimensional QED and QCD

TL;DR

This paper reviews the phase structures of two-dimensional QED and QCD, showing that QCD's phase is unaffected by theta vacuum, unlike QED, with implications for confinement and screening phases.

Contribution

It reformulates non-abelian QCD to resemble the Schwinger model and compares their phase structures, highlighting differences in theta vacuum effects.

Findings

QED exhibits different phases for massless and massive cases.

QCD's phase structure is unaffected by theta vacuum.

Massless QED is in the screening phase, massive QED is confining, while QCD remains in the screening phase.

Abstract

The semi-classical phase structure of two-dimensional QED and QCD are briefly reviewed. The non-abelian theory is reformulated to closely resemble the Schwinger model. It is shown that, contrary to the abelian theory, the phase structure of two-dimensional QCD is unaffected by the structure of the theta vacuum. We make parallel calculations in the two theories and conclude that massless Schwinger model is in the screening and the massive theory is in the confining phase, whereas both massless and massive QCD are in the screening phase.