An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge

TL;DR

This paper explores a dynamical mechanism for generating off-diagonal gluon and ghost masses in SU(N) Yang-Mills theories within the maximal Abelian gauge, supporting the Abelian dominance hypothesis.

Contribution

It introduces a novel approach linking mass generation to a mixed gluon-ghost condensate and connects it with the <A^2> condensate, using algebraic renormalization techniques.

Findings

Mass generation lowers vacuum energy.

Gauge parameter independence confirmed.

Connection established with <A^2> condensate.

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 the 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.