Gauge fixing and extended Abelian monopoles in SU(2) gauge theory in 2+1 dimensions

Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in three dimensions. Monopoles are computed by Abelian projection in several gauges, including the maximal Abelian gauge. The number ${\mathit{N}}_{\mathit{m}}$ of extended monopoles in a cube of size ${\mathit{m}}^3$ (in lattice units) is defined as the number of elementary ($1^3$) monopoles minus antimonopoles in the cube (m=1,2,...). The distribution of $1^3$ monopoles in the nonlocal maximal Abelian gauge is shown to be essentially random, while nonscaling of the density of $1^3$ monopoles in some local gauges, which has been previously observed, is shown to be mainly due to strong short-distance correlations. The density of extended monopoles in local gauges is studied as a function of β for monopoles of fixed physical ‘‘size’’ (m/β=fixed); the degree of scale violation is found to decrease substantially as the monopole size is increased. The possibility therefore remains that long-distance properties of monopoles in local gauges may be relevant to continuum physics, such as confinement.