Gribov copies in the maximally Abelian gauge and confinement

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 {open_quotes}condensates.{close_quotes} 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 {open_quotes}extreme{close_quotes} Gribov copies also differ but this difference appears to be no more than about 20{percent}. 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. {copyright} {ital 1997} {ital The American Physical Society}