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We study the dependence of the center-projected string tension on both the lattice size, and the number of gauge copies used for maximal center gauge fixing. We show that a recent finding of Bornyakov, Komarov, Polikarpov, and Veselov (hep-lat/0002017), indicating a substantial breakdown of center dominance in maximal center gauge, is only obtained for rather small lattice volumes, and is not found in numerical simulations on larger lattices. It is shown that center-projected Creutz ratios approach the full asymptotic string tension as lattice size increases, and that the P-vortex density is consistent, at moderately weak couplings, with 2-loop scaling behavior. [ABSTRACT FROM AUTHOR]

We investigate the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature. In center projection the vortices (called P-vortices) form connected two dimensional surfaces on the dual four-dimensional lattice. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. All of the huge vortices detected in several thousand field configurations turn out to be unorientable. We determine the Euler characteristic of these surfaces and find that they have a very irregular structure with many handles. At finite temperature P-vortices exist also in the deconfined phase. They form cylindric objects which extend in time direction. After removal of unimportant short range fluctuations they consist only of space-space plaquettes, which is in accordance with the perimeter law behaviour of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in this phase. [ABSTRACT FROM AUTHOR]

We consider projections of SU(2) lattice link variables onto Z2 center and U(1) subgroups, with and without gauge-fixing. It is shown that in the absence of gauge-fixing, and up to an additive constant, the static quark potential extracted from projected variables agrees exactly with the static quark potential taken from the full link variables; this is an extension of recent arguments by Ambjørn and Greensite, and by Ogilvie. Abelian and center dominance is essentially trivial in this case, and seems of no physical relevance. The situation changes drastically upon gauge fixing. In the case of center projection, there are a series of tests one can carry out, to check if vortices identified in the projected configurations are physical objects. All these criteria are satisfied in maximal center gauge, and we show here that they all fail in the absence of gauge fixing. The non-triviality of center projection is due entirely to the maximal center gauge-fixing, which pumps information about the location of extended physical objects into local Z2 observables. [ABSTRACT FROM AUTHOR]