On the infrared behaviour of Gluons and Ghosts in Ghost-Antighost symmetric gauges

TL;DR

This paper investigates the infrared behavior of gluon and ghost propagators in various covariant gauges, finding no evidence for ghost-antighost condensates and highlighting challenges in symmetric gauges.

Contribution

It derives Dyson--Schwinger equations in covariant gauges, analyzes their infrared behavior, and explores implications for ghost-antighost condensates in Yang--Mills theories.

Findings

Infrared suppressed gluon propagator in covariant gauges

Infrared enhanced ghost propagator in covariant gauges

No evidence for ghost-antighost condensate in studied gauges

Abstract

To investigate the possibility of a ghost-antighost condensate the coupled Dyson--Schwinger equations for the gluon and ghost propagators in Yang--Mills theories are derived in general covariant gauges, including ghost-antighost symmetric gauges. The infrared behaviour of these two-point functions is studied in a bare-vertex truncation scheme which has proven to be successful in Landau gauge. In all linear covariant gauges the same infrared behaviour as in Landau gauge is found: The gluon propagator is infrared suppressed whereas the ghost propagator is infrared enhanced. This infrared singular behaviour provides indication against a ghost-antighost condensate. In the ghost-antighost symmetric gauges we find that the infrared behaviour of the gluon and ghost propagators cannot be determined when replacing all dressed vertices by bare ones. The question of a BRST invariant dimension two condensate remains to be further studied.