arXiv subjects
Publications and source records attributed to John D. Stack.
We introduce a generalized Maximum Abelian Gauge (MAG). We work with this new gauge on 12^4 lattices for beta=5.7,5.8 and 16^4 lattices for beta=5.9,6.0. We also introduce a form of abelian projection related to the generalized MAG. We measure U(1)xU(1) wilson loops and single color magnetic current densities.
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)xU(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)xU(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 general problem of obtaining reliable results from gauge-fixing and projection is discussed. It is shown that the usual form of the maximal abelian gauge gives poor results for the string tension in SU(3) lattice gauge theory. A generalized form is suggested. Evidence is presented that monopoles in SU(3) are associated with SU(2) subgroups, and that P-vortices pass through monopoles, similar to what happens in SU(2).
We gauge fix 600 SU(3) beta=6.0 configurations on a 16^4 lattice to a simple form of the maximal abelian gauge. We project the SU(3) valued links to the U(1)xU(1) subgroup, and extract U(1)xU(1) and monopole string tensions. After gauge fixing to the indirect center gauge, the U(1)xU(1) links are projected to Z(3) and a vortex string tension is measured. The vortex and magnetic current densities are measured.
We study monopoles and vortices in SU(2) lattice gauge theory on a 24**4 lattice at beta=2.50. We find a value of fundamental string tension from monopoles in the maximum Abelian gauge consistent with the full SU(2) value. Using direct and indirect center gauges, we find fundamental string tension values from P-vortices which are larger than the full SU(2) result. After a single cooling sweep, the string tensions from monopoles and P-vortices are all 30% lower than the full SU(2) value, while the U(1) string tension in the maximum Abelian gauge remains consistent with the full SU(2) result. Blocking the lattice after cooling does not restore the low values of string tension found with monopoles and vortices.
We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.
We study the heavy quark potential in the SU(2) positive plaquette model using monopoles in the maximum abelian gauge, and vortices. Monopoles give a quantitative description of the string tension. Vortices approximately reproduce the entire heavy quark potential.
We investigate the masses of 0+ and 2+ glueballs in SU(2) lattice gauge theory using abelian projection to the maximum abelian gauge. We calculate glueball masses using both abelian links and monopole operators. Both methods reproduce the known full SU(2) results quantitatively. Positivity problems present in the abelian projection are discussed. We study the dependence of the glueball masses on magnetic current loop size, and find that the 0+ state requires a much greater range of sizes than does the 2+ state.
We present results suggesting that magnetic monopoles can account for chiral symmetry breaking in abelian gauge theory. Full U(1) configurations from a lattice simulation are factorized into magnetic monopole and photon contributions. The expectation is computed using the monopole configurations and compared to results for the full U(1) configurations. It is shown that excellent agreement between the two values of is obtained if the effect of photons, which "dress" the composite operator psibarpsi, is included. This can be estimated independently by measurements of the physical fermion mass in the photon background.
We present results from magnetic monopoles in $SU(2)$ lattice gauge theory at finite temperature. The lattices are $16^{3}\times N_{t}$, for $N_{t}=4,6,8,12$, at $β=2.5115$. Quantities discussed are: the spacial string tension, Polyakov loops, and the screening of timelike and spacelike magnetic currents.
We resolve a discrepancy between the SU(2) spacial string tension at finite temperature, and the value obtained by monopoles in the maximum Abelian gauge. Previous work had incorrectly omitted a term due to Dirac sheets. When this term is included, the monopole and full SU(2) determinations of the spacial string tension agree to within the statistical errors of the monopole calculation.
Confinement via 't Hooft-Mandelstam monopoles is studied for the positive plaquette model in SU(2) lattice gauge theory. Positive plaquette model configurations are projected into the maximum abelian gauge and the magnetic current extracted. The resulting magnetic current is used to compute monopole contributions to Wilson loops and extract a monopole contribution to the string tension. As was previously found for the Wilson action, the monopole contribution to the string tension agrees with the string tension calculated directly from the SU(2) links. The fact that the positive plaquette model suppresses Z2 monopoles and vortices is discussed.
The axis for Figure 2 was wrong. It has been fixed and the postscript file replaced (The file was called comp.ps).