Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian 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 µ , which has attracted much attention in the Landau gauge.

Gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: Taking into account the effects of the Gribov copies and of the dimension two condensates

“…In this paper we focus on the gluon and ghost propagators in the maximal Abelian gauge [1,2,3], which we are investigating since several years [4,5,6,7,8,9,10,11,12,13,14]. In our previous works we have provided analytical evidence of nonperturbative effects which should be taken into account when facing the various features displayed by this gauge, such as the dual superconductivity picture for color confinement [15] and the Abelian dominance hypothesis [16,17,18,19].…”

Study of the nonlocal gauge invariant mass operator $\mathrm{Tr} \int d^4x F_{μν} (D^2)^{-1} F_{μν}$ in the maximal Abelian gauge

“…Let us turn our attention to the characterization of the most general invariant counterterm Σ CT which can be freely added to Σ. According to the algebraic renormalization procedure [58], we require that the perturbed action (Σ + ǫΣ CT ) satisfy the same set of Ward identities, (46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61)(62), and constraints of Σ. The counterterm Σ CT must be an integrated local polynomial in the fields and sources with dimension bounded by four, vanishing ghost number and Q 6 -charge, obeying the following constraints…”

“…In an attempt to understand those lattice results in the MAG, also here the condensation of dimension two operators has been considered. In [37,49], a dynamical mass generation mechanism for the off-diagonal gluons was proposed in the MAG, by means of the condensation of the operator 1 2 A a µ A a µ + αc a ca 1 .…”

Study of the nonlocal gauge invariant mass operator Tr∫d4xFμν(D2)−1Fμνin the maximal Abelian gauge

“…In an attempt to understand those lattice results in the MAG, here also the condensation of dimension two operators has been considered. In [37,49], a dynamical mass generation mechanism for the off-diagonal gluons was proposed in the MAG, by means of the condensation of the operator 1 2 A a µ A a µ + α ca ca . 4 As the reader may have noticed, the dimension two operators mentioned above are gauge dependent, being related to specific choices of the gauge fixing.…”