Gauge Fixing and Extended Abelian Monopoles in SU(2) Gauge Theory in 2+1 Dimensions

Abstract

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 $N_m$ of extended monopoles in a cube of size $m^3$ (in lattice units) is defined as the number of elementary ($1^3$) monopoles minus antimonopoles in the cube ($m=1,2,\dots$). 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 $\beta$ for monopoles of fixed physical ``size'' ($m/\beta =\mathrm{fixed}$); 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.

Revised version, hep-lat/9312008. 9 pages (revtex 3.0). 8 Figures. All enclosed as uuencoded script. IN THIS VERSION WE CONSIDER TYPE II EXTENDED MONOPOLES. IN THE ORIGINAL MANUSCRIPT WE CONSIDERED TYPE I EXTENDED MONOPOLES

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Cited by in corpus (6)

• Chiral Symmetry Breaking in Abelian-Projected SU(2) Lattice Gauge Theory
• Structure and Dynamics of Monopoles in Axial-Gauge QCD
• Abelian dominance and adjoint sources in lattice QCD
• Abelian Dominance of Chiral Symmetry Breaking in Lattice QCD
• Scaling and confinement aspects of tadpole improved SU(2) lattice gauge theory and its abelian projection
• Abelian Dominance in Chiral Symmetry Breaking