A remark on the BRST symmetry in the Gribov-Zwanziger theory

TL;DR

This paper demonstrates how to reformulate the BRST symmetry breaking in the Gribov-Zwanziger theory into a linear form using auxiliary fields, enabling better control over renormalization through Slavnov-Taylor identities.

Contribution

It introduces a method to convert soft BRST breaking into linear breaking in the Gribov-Zwanziger theory, facilitating renormalization analysis.

Findings

BRST symmetry breaking can be linearized with auxiliary fields

Linear breaking allows derivation of Slavnov-Taylor identities

Renormalization can be studied via cohomology of a nilpotent operator

Abstract

We show that the soft breaking of the BRST symmetry arising in the Gribov-Zwanziger theory can be converted into a linear breaking upon introduction of a set of BRST quartets of auxiliary fields. Due to its compatibility with the Quantum Action Principle, the linearly broken BRST symmetry can be directly converted into a suitable set of useful Slavnov-Taylor identities. As a consequence, it turns out that the renormalization aspects of the Gribov-Zwanziger theory can be addressed by means of the cohomology of a nilpotent local operator