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

Abstract

Ghost condensates of dimension two in SU (N ) Yang-Mills theory quantized in the Maximal Abelian Gauge are discussed. These condensates turn out to be related to the dynamical breaking of the SL(2, R) symmetry present in this gauge.

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.…”

Propagators, running coupling and condensates in lattice QCD

“…In recent years, (gauge-dependent) condensates of mass di-mension two have also received considerable attention [29,[70][71][72][73][74][75][76][77][78][79][80][81][82]. In particular, the gauge condensate A b µ A b µ has been largely studied, since it should be sensitive to topological structures such as monopoles [70] and it could play an important role in the quark-confinement scenario through monopole condensation [83].…”

Ghost condensation on the lattice

“…These condensates were first introduced in SU (2) gauge theory in maximally Abelian gauge (MAG) [7,10,27,32,39,40,41]. More recently, the same condensates have been studied in other gauges [6,8,9,13,28,30], such as the CurciFerrari and the Landau gauges.…”

“…In all cases it was found that the ghost condensates are related to the breakdown of a global SL(2, R) symmetry [6,42]. In MAG the diagonal and off-diagonal components of the ghost propagators are modified [7,27] by ghost condensation. Similar results have been obtained in other gauges [13,30].…”