Masslessness of ghosts in equivariantly gauge-fixed Yang--Mills theories

TL;DR

This paper demonstrates that ghosts remain massless at one-loop in equivariantly gauge-fixed Yang--Mills theories, confirming that symmetry forbids ghost mass generation and highlighting the role of four-ghost interactions.

Contribution

It explicitly calculates the one-loop ghost self-energy, confirming the masslessness of ghosts due to equivariant BRST symmetry in these theories.

Findings

Ghost self-energy vanishes at zero momentum

Ghost mass is forbidden by symmetry

Four-ghost interactions are essential for this result

Abstract

We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang--Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang--Mills theory is needed in order to obtain this result.