Ghost Condensates in Yang–mills Theories in Nonlinear Gauges

Abstract

Ghost condensates of dimension two are analyzed in a class of nonlinear gauges in pure Yang–Mills theories. These condensates are related to the breaking of the SL (2, R) symmetry, present in these gauges.

Ghost condensates and dynamical breaking ofSL(2,R) in Yang–Mills in the maximal Abelian gauge

“…It is worth mentioning that by now evidences for the ghost condensation have been reported in other gauges, namely in the Curci-Ferrari gauge [27,28,29] and in the Landau gauge [30]. All these gauges, including the Maximal Abelian Gauge, possess a global SL(2, R) symmetry [18], a feature which seems to be deeply related to the ghost condensation.…”

Unphysical nature of theSL(2,R)symmetry and its associated condensates in Yang-Mills theories

“…Hence, these symmetries are trivial for YM [8,17] and therefore can not be of any physical relevance. As SL(2, R) is not a symmetry of YM there is no physical justification to impose to the quantum theory Ward identities associated with it [3]. The expectation that there is a physical meaning attached to the symmetry breaking of SL(2, R) by ghost condensates loses all its support in view of this analysis.…”

“…In recent years there has been a growing interest in condensates of functionals of mass dimension two in SU (N ) Yang-Mills (YM) theories in four dimensions involving ghost fields [1,2,3]. The condensates are signaled by nonvanishing expectation values of the functionals.…”

“…Also in the CF gauge the breaking of an SL(2, R) symmetry has been associated with ghost condensates [3]. The mass generated by this condensation scenario was later shown to be tachyonic [4].…”

Three loop bar Mbar S renormalization of QCD in the maximal abelian gauge

“…Significantly, similar identities for the analogous operator exist in other gauges such as the maximal abelian gauge (MAG), [15,16], and in space-time dimensions other than four, [17]. Since these dimension two operators have been the subject of intense analytic investigation in various gauges in recent years, see, for instance [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] and references therein, due to their condensation in a non-trivial vacuum, there is a clear need to renormalize QCD in this gauge. In particular the explicit values of all the anomalous dimensions are required as the first step in the extension of the local composite operator (LCO) method for QCD, [18], to the MAG in various colour groups.…”