Scaling and confinement aspects of tadpole improved SU(2) lattice gauge theory and its Abelian projection

Abstract

Using a tadpole-improved SU(2) gluodynamics action, the non-Abelian potential and the Abelian potential after the Abelian projection are computed. Rotational invariance is found restored at coarse lattices both in the non-Abelian theory and in the effective Abelian theory resulting from the maximal Abelian projection. Asymptotic scaling is tested for the SU(2) string tension. Deviation of the order of 6% is found for lattice spacings between 0.27 and 0.06 fm. Evidence for asymptotic scaling and scaling of the monopole density in maximal Abelian projection is also seen, but not at coarse lattices. The scaling behavior is compared with analyses of Wilson action results, using bare and renormalized coupling schemes. Using extended monopoles, evidence is found that the gauge dependence of the Abelian projection reflects short distance fluctuations, and may thus disappear at large scales.