On ghost condensation, mass generation and Abelian dominance in the Maximal Abelian Gauge

TL;DR

This paper critically examines ghost condensation in the Maximal Abelian Gauge, arguing it cannot explain off-diagonal gluon mass generation and Abelian dominance, and discusses alternative mechanisms for real mass generation.

Contribution

It challenges previous claims linking ghost condensation to gluon mass and Abelian dominance, proposing the need for alternative explanations.

Findings

Ghost condensation leads to tachyonic mass, not real mass.

Ghost condensation cannot be the cause of Abelian dominance.

Alternative mechanisms are necessary for real mass generation.

Abstract

Recent work claimed that the off-diagonal gluons (and ghosts) in pure Yang-Mills theories, with Maximal Abelian gauge fixing (MAG), attain a dynamical mass through an off-diagonal ghost condensate. This condensation takes place due to a quartic ghost interaction, unavoidably present in MAG for renormalizability purposes. The off-diagonal mass can be seen as evidence for Abelian dominance. We discuss why ghost condensation of the type discussed in those works cannot be the reason for the off-diagonal mass and Abelian dominance, since it results in a tachyonic mass. We also point out what the full mechanism behind the generation of a real mass might look like.