P-vortices and drama of Gribov copies

Bornyakov, V. G.; Комаров, Д. А.; Polikarpov, M.I.

doi:10.1016/s0370-2693(00)01309-5

Cited by 60 publications

(89 citation statements)

References 29 publications

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“…These configurations are known as Gribov copies. Difficulties associated with Gribov copies in maximal center gauge have been noted in recent work by Bornyakov et al [1,2], and previously by Kovács and Tomboulis [3]. In this article we discuss some issues that we believe are relevant to the problem of generating a set of Gribov copies in maximal center gauge, and to choosing the "best" Gribov copy among the set.…”

Section: Introductionmentioning

confidence: 77%

“…We see that, according to the criterion of minimizing the average δ 2 , simulated annealing gives the best fit to a thin vortex, the KT method is a little worse, and OR is the worst of the three, as already noted in ref. [1]. There is something a little peculiar about this ordering, however.…”

Section: Quenched Vs Annealed Gribov Copiesmentioning

confidence: 96%

“…[8]. Simulated annealing is achieved by applying Metropolis updates to the analog spin system, and gradually lowering the temperature variable from some initial value to zero [1]. Neither of these methods obtains the true minimum of H; each generates a set of Gribov copies in maximal center gauge.…”

Section: Quenched Vs Annealed Gribov Copiesmentioning

confidence: 99%

“…Instead of applying over-relaxation to a random point on the gauge orbit of a thermalized configuration, they first fixed the configuration to ordinary lattice Landau gauge, and then applied over-relaxation to fix to maximal center gauge. We will refer to the quenching procedure via over-relaxation described in [8] as "OR", the Kovács-Tomboulis variation of this procedure as "KT", and simulated annealing, studied in maximal center gauge by Bornyakov et al [1], as "SA".…”

Section: Quenched Vs Annealed Gribov Copiesmentioning

confidence: 99%

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Remarks on the Gribov problem in the direct maximal center gauge

Faber¹,

Greensite²,

Olejník³

2001

Phys. Rev. D

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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.

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Section: Introductionmentioning

confidence: 77%

Section: Quenched Vs Annealed Gribov Copiesmentioning

confidence: 96%

Section: Quenched Vs Annealed Gribov Copiesmentioning

confidence: 99%

Section: Quenched Vs Annealed Gribov Copiesmentioning

confidence: 99%

See 2 more Smart Citations

Remarks on the Gribov problem in the direct maximal center gauge

Faber¹,

Greensite²,

Olejník³

2001

Phys. Rev. D

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“…(4). No individual adjoint Higgs field can give equal coefficients for the various charged vector fields in the functional.…”

Section: Generalized Maximal Abelian Gaugementioning

confidence: 99%

The maximal abelian gauge, monopoles, and vortices in SU(3) lattice gauge theory

2002

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We report on calculations of the heavy quark potential in SU(3) lattice gauge theory. Full SU(3) results are compared to three cases which involve gauge-fixing and projection. All of these start from the maximal abelian gauge (MAG), in its simplest form. The first case is abelian projection to U(1) × U(1). The second keeps only the abelian fields of monopoles in the MAG. The third involves an additional gauge-fixing to the indirect maximal center gauge (IMCG), followed by center projection to Z(3). At one gauge fixing/configuration, the string tensions calculated from MAG U(1) × U(1), MAG monopoles, and IMCG Z(3) are all less than the full SU(3) string tension. The projected string tensions further decrease, by approximately 10%, when account is taken of gauge ambiguities. Comparison is made with corresponding results for SU(2). It is emphasized that the formulation of the MAG is more subtle for SU(3) than for SU(2), and that the low string tensions may be caused by the simple MAG form used. A generalized MAG for SU(3) is formulated.

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Status of Center Dominance in Various Center Gauges

Faber

Greensite

Olejník

2002

Confinement, Topology, and Other Non-Perturbative Aspects of QCD

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We review arguments for center dominance in center gauges where vortex locations are correctly identified. We introduce an appealing interpretation of the maximal center gauge, discuss problems with Gribov copies, and a cure to the problems through the direct Laplacian center gauge. We study correlations between direct and indirect Laplacian center gauges. Why Center Dominance?The aim of most lattice studies of the confinement mechanism is to extract from lattice link variables the most relevant parts for the infrared dynamics. The concept of (some kind of) dominance seems a necessary, though not sufficient, condition for success. If we extract the (would-be) relevant parts of links and compute physical quantities related to confinement (e.g. the string tension) we expect to reproduce their behavior in the full theory. Were it not the case, one could hardly claim to have achieved the goal.

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P-vortices and drama of Gribov copies

Cited by 60 publications

References 29 publications

Remarks on the Gribov problem in the direct maximal center gauge

Remarks on the Gribov problem in the direct maximal center gauge

The maximal abelian gauge, monopoles, and vortices in SU(3) lattice gauge theory

Status of Center Dominance in Various Center Gauges

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