Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge

TL;DR

This paper explores a mechanism for dynamical mass generation of off-diagonal gluons and ghosts in SU(N) Yang-Mills theories within the maximal Abelian gauge, supporting the concept of Abelian dominance.

Contribution

It introduces a novel mass generation mechanism via a mixed gluon-ghost condensate and connects it to the vacuum energy associated with the <A^2> condensate.

Findings

Mass generation from gluon-ghost condensate lowers vacuum energy.

Results are gauge parameter independent.

Connects vacuum energy to <A^2> condensate in Landau gauge.

Abstract

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension two condensate discussed here, with the non-trivial vacuum energy originating from the condensate <A^2>, which has attracted much attention in the Landau gauge.