The Gribov horizon and spontaneous BRST symmetry breaking

TL;DR

This paper reformulates the Gribov-Zwanziger theory to incorporate gauge fixing ambiguities, revealing spontaneous BRST symmetry breaking and exploring its implications for gauge invariance, renormalization, and unitarity in confining gauge theories.

Contribution

It introduces an algebraic approach to spontaneous BRST symmetry breaking within the Gribov horizon, enabling the use of cohomology tools for gauge invariant operator analysis.

Findings

BRST symmetry is spontaneously broken due to the Gribov horizon.

The Goldstone sector decouples from the physical spectrum.

BRST cohomology alone does not guarantee unitarity in confining theories.

Abstract

An equivalent formulation of the Gribov-Zwanziger theory accounting for the gauge fixing ambiguity in the Landau gauge is presented. The resulting action is constrained by a Slavnov-Taylor identity stemming from a nilpotent exact BRST invariance which is spontaneously broken due to the presence of the Gribov horizon. This spontaneous symmetry breaking can be described in a purely algebraic way through the introduction of a pair of auxiliary fields which give rise to a set of linearly broken Ward identities. The Goldstone sector turns out to be decoupled. The underlying exact nilpotent BRST invariance allows to employ BRST cohomology tools within the Gribov horizon to identify renormalizable extensions of gauge invariant operators. Using a simple toy model and appropriate Dirac bracket quantization, we discuss the time-evolution invariance of the operator cohomology. We further comment on the unitarity issue in a confining theory, and stress that BRST cohomology alone is not sufficient to ensure unitarity, a fact, although well known, frequently ignored.