Remarks on the Gribov problem in the direct maximal center gauge

Abstract

Abstract:We review the equivalence of maximal center gauge fixing to the problem of finding the best fit, to a given lattice gauge field, by a thin vortex configuration. This fit is necessarily worst at the location of P-plaquettes. We then compare the fits achieved in Gribov copies generated by (i) over-relaxation; (ii) over-relaxation after Landau gauge preconditioning; and (iii) simulated annealing. Simulated annealing yields the best fit if all links on the lattice are included, but the situation changes if we consider only the lattice volume exterior to P-plaquettes. In this exterior region, the fit is best for Gribov copies generated by over-relaxation, and worst for Gribov copies generated after Landau gauge preconditioning. The two fitting criteria (including or not including the P-plaquettes) yield string tensions differing by −34% to +20% respectively, relative to the full string tension. Our usual procedure ("quenched minimization") seems to be a compromise between these criteria, and yields string tensions at an intermediate value close to the full string tension.

The confinement problem in lattice gauge theory

“…One criticism that can be leveled against the center projection data presented here is that the agreement of the center projected and full string tensions varies widely among different adjoint gauges, and among Gribov copies in the same adjoint gauge [103,104,105,106,107,108,77]. DMC gauge, for example, when fixed by the over-relaxation procedure, has very good center dominance properties, with disagreement between full and projected string tensions on the order of a few percent [106].…”

Magnetic monopoles in the high temperature phase of Yang–Mills theories

“…As we have emphasized above, very similar problems are met when studying center dominance in the maximal center gauge (MCG) [22][23][24][25] and some possible interpretations have been discussed [24,26]. One should also study how the problem is related to the choice of a particular starting point on the gauge orbit (belonging to Landau gauge in our case) and perform more extensive studies in which the global maximum of the MAG functional is searched for via better algorithms, like for instance simulated annealing [27].…”

“…We have however a further warning. We have tried the following experiment, which is not new and has been performed previously in the literature, even if mostly in the context of center dominance studies [22][23][24][25]. We have repeated part of our measurements, using again the Maximal Abelian gauge in order to define the abelian projection, but using a sample of configurations which had been previously fixed to Landau gauge.…”

Properties of P-vortices and monopole clusters in latticeSU(2)gauge theory

“…It appears that near the continuum limit for IMCP and DMCP σ Z(2) /σ SU (2) is of the order of 0.6. Probably to reproduce the full string tension from Z(2) variables we have to use some other Z(2) projection [16]. In any case the fact that we reproduce a substantial part of the string tension from Z(2) variables shows that P-vortices even in the considered projections are related to the confinement.…”

“…There has been a long discussion in the literature on whether the P-vortices reproduce well the non-Abelian string tension (see Refs. [8], [15], [16], [17] and references therein). On Fig.…”