BRST Cohomology and Physical Space of the GZ Model

TL;DR

This paper investigates BRST symmetry breaking in the GZ model of QCD, showing that breaking occurs mainly in unphysical sectors and proposing conditions under which BRST symmetry remains intact for physical observables, supporting confinement.

Contribution

It provides a detailed analysis of BRST symmetry breaking in the GZ model and proposes a criterion for operators that preserve BRST, clarifying the physical state space.

Findings

BRST breaking is confined to unphysical sectors

BRST-exact parts of key operators have zero expectation value

The horizon condition and Kugo-Ojima criterion imply confinement

Abstract

We address the issue of BRST symmetry breaking in the GZ model, a local, renormalizable, non-perturbative approach to QCD. Explicit calculation of several examples reveals that BRST symmetry breaking apparently afflicts the unphysical sector of the theory, but may be unbroken where needed, in cases of physical interest. Specifically, the BRST-exact part of the conserved energy-momentum tensor and the BRST-exact term in the Kugo-Ojima confinement condition both have vanishing expectation value. We analyze the origin of the breaking of BRST symmetry in the GZ model, and obtain a useful sufficient condition that determines which operators preserve BRST. Observables of the GZ theory are required to be invariant under a certain group of symmetries that includes not only BRST but also others. The definition of observables is thereby sharpened, and excludes all operators known to us that break BRST invariance. We take as a hypothesis that BRST symmetry is unbroken by this class of observables. If the hypothesis holds, BRST breaking is relegated to the unphysical sector of the GZ theory, and its physical states are obtained by the usual cohomological BRST construction. The fact that the horizon condition and the Kugo-Ojima confinement criterion coincide assures that color is confined in the GZ theory.