We calculate the heavy quark potential from the magnetic current due to monopoles in four dimensional SU(2) lattice gauge theory. The magnetic current is located in configurations generated in a conventional Wilson action simulation on a 16 4 lattice. The configurations are projected with high accuracy into the maximum abelian gauge. The magnetic current is then extracted and the monopole contribution to the potential is calculated. The resulting string tension is in excellent agreement with the SU(2) string tension obtained by conventional means from the configurations. Comparison is made with the U(1) case, with emphasis on the differing periodicity properties of SU(2) and U(1) lattice gauge theories. The properties of the maximum abelian gauge are discussed.

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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.

The string tension is calculated using magnetic monopoles in three-dimensional U(l) lattice gauge theory. The monopoles are identified in configurations of link angles generated in a simulation on a 32 3 lattice. Wilson-loop values are determined by the monopoles' flux through the loop. The string-tension results are in excellent agreement with a semiclassical analytic formula. PACS numbers: 11.15.Ha, 14.80.HvHow is the topology of the vacuum related to confinement? A quantitative answer to this question has been elusive for lattice QCD. In this paper, we report on numerical calculations for the case of U(l) lattice gauge theory in three dimensions. Our principal result is a calculation of the string tension which directly involves magnetic monopoles.The physics studied here was first discussed by Polyakov 1,2 who considered a three-dimensional continuum theory in which the essential feature was an unbroken U(l) gauge group with monopoles as instantons. Electric confinement was established by a semiclassical analysis of the multimonopole gas. In an analogous lattice treatment, Banks, Myerson, and Kogut derived an explicit formula for the string tension in Villain's version of the U(l) theory. 3 Our simulations establish that this formula for the string tension is accurate over an unexpectedly wide range of couplings.To begin our calculations, values of Wilson loops were gathered on a 32 3 lattice. 4 Because it is efficient to simulate, we used the cosine form of the U(l) action: 50.70 > 0 0.00 o.o 10.0 R/a FIG. 1. The potentials from the original Wilson loops and their linear-plus-Coulomb fits.whereand a is the lattice spacing. A heat-bath algorithm was used to update the links. 6 Wilson-loop statistics were enhanced with an analytic version of the multihit procedure of Parisi, Petronzio, and Rapuano. 7 At Pw sss 2.0, 2.2, and 2.4, we made runs of 25000 sweeps, dropped the first 5000, and measured all Wilson loops up to R -10axr-"14