Gribov Copies in the Maximally Abelian Gauge and Confinement

Abstract

We fix $SU(2)$ lattice gauge fields to the Maximally Abelian gauge in both three and four dimensions. We extract the corresponding $U(1)$ fields and monopole current densities and calculate separately the confining string tensions arising from these $U(1)$ fields and monopole `condensates'. We generate multiple Gribov copies and study how the $U(1)$ fields and monopole distributions vary between these different copies. As expected, we find substantial variations in the number of monopoles, their locations and in the values of the $U(1)$ field strengths. The string tensions extracted from `extreme' Gribov copies also differ but this difference appears to be no more than about 20\%. We also directly compare the fields of different Gribov copies. We find that on the distance scales relevant to confinement the $U(1)$ and monopole fluxes that disorder Wilson loops are highly correlated between these different Gribov copies. All this suggests that while there is indeed a Gribov copy problem the resulting ambiguity is, in this gauge and for the study of confinement, of limited importance.

31 pages LaTeX plus 5 PostScript figures. Uses epsf.sty. Self-unpacking, uuencoded tar-compressed file

References in corpus (3)

• Dual Superconductor Scenario of Confinement: A Systematic Study of Gribov Copy Effects
• String Tension from Monopoles in SU(2) Lattice Gauge Theory
• Dirac sheets and gauge fixing in $U(1)$ lattice gauge theory

Cited by in corpus (10)

• Problems in Lattice Gauge Fixing
• Monopole clusters in Abelian projected gauge theories
• Geometry of the physical phase space in quantum gauge models
• Instantons and Gribov Copies in the Maximally Abelian Gauge
• Monopole clusters, Z(2) vortices and confinement in SU(2)
• Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories
• Abelian projected SU(2) Yang-Mills action for renormalisation group flows
• The Configuration Space of Low-dimensional Yang-Mills Theories
• Ehrenfest theorems and charge antiscreening in Abelian projected gauge theories
• Abelian Links, Monopoles and Glueballs in SU(2) Lattice Gauge Theory