Equation of state of gluon plasma and renormalization of local action

Abstract

We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRSTinvariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Lindé and which occur in the order g 6 corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections. Renormalization and renormalization-group flow are described. We calculate the ghost propagator and color-Coulomb potential to one-loop and find that they are long range, whereas the 3-dimensionally transverse would-be physical gluon propagator is suppressed like k 2 at small |k|. These one-loop results accord with the Gribov scenario in Coulomb gauge and with recent numerical determinations of these quantities. When the auxiliary fields are integrated out, one obtains the standard Coulomb gauge action with a cut-off at the Gribov horizon.

Study of the properties of the Gribov region inSU(N) Euclidean Yang–Mills theories in the maximal Abelian gauge

“…In order to obtain an explicit expression for V( ), we make use of the so-called no-pole condition [1], which is a condition on the connected two-point function of the off-diagonal Faddeev-Popov ghost fields. As pointed out in [1], see also [50] for a pedagogical introduction, the no-pole condition stems from the positivity of the Faddeev-Popov operator, M ab > 0, within the Gribov region , according to equation (29). As a consequence, within , the operator M ab is invertible.…”

“…In equation (29), we defined the region as the set of fields fulfilling the maximal Abelian gauge conditions and for which the operator M ab is positive definite. Let us now establish some properties of this region.…”

“…As pointed out in [28], the existence of the Gribov copies is in fact a general feature of the gauge-fixing procedure. Besides the Landau gauge, the issue of the Gribov copies has been addressed in other gauges such as the Coulomb gauge [29] and the linear covariant gauge [30], which has the Landau gauge as a particular case. Concerning the maximal Abelian gauge, only the particular case of SU (2) has been discussed so far [31,32].…”