The `BRST-invariant' Condensate of Dimension Two in QCD

TL;DR

This paper discusses the nature and gauge invariance of a specific dimension-two condensate in QCD, emphasizing its invariance under an on-shell BRST symmetry that includes partial gauge fixing.

Contribution

It clarifies the status of the BRST-invariant condensate in QCD and identifies gauge-invariant operators corresponding to it in different gauges.

Findings

The condensate is invariant under an on-shell BRST symmetry including partial gauge fixing.

Gauge-invariant operators corresponding to the condensate are identified in Lorentz and maximal Abelian gauges.

These operators are invariant under residual gauge transformations.

Abstract

The status of the `BRST-invariant' condensate of mass dimension two in QCD is explained. The condensate is only invariant under an `on-shell' BRST symmetry which includes a partial gauge-fixing. The on-shell BRST symmetry represents the residual gauge symmetry under gauge transformations which preserve the partial gauge fixing. The gauge-invariant operators which correspond to the BRST-invariant condensate are identified in the Lorentz and maximal Abelian gauges and are shown to be invariant under the residual gauge transformations.