We find, in close analogy to Abelian dominance in the maximal Abelian gauge, the phenomenon of center dominance in the maximal center gauge for SU͑2͒ lattice gauge theory. The maximal center gauge is a gauge-fixing condition that preserves a residual Z 2 gauge symmetry; ''center projection'' is the projection of SU͑2͒ link variables onto Z 2 center elements, and ''center dominance'' is the fact that the center-projected link elements carry most of the information about the string tension of the full theory. We present numerical evidence that the thin Z 2 vortices of the projected configurations are associated with ''thick'' Z 2 vortices in the unprojected configurations. The evidence also suggests that the thick Z 2 vortices may play a significant role in the confinement process. ͓S0556-2821͑97͒07104-X͔

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We discuss the implementation of the "direct" maximal center gauge (a gauge which maximizes the lattice average of the squared-modulus of the trace of link variables), and its use in identifying Z 2 center vortices in Yang-Mills vacuum configurations generated by lattice Monte Carlo. We find that center vortices identified in the vacuum state account for the full asymptotic string tension. Scaling of vortex densities with lattice coupling, change in vortex size with cooling, and sensitivity to Gribov copies is discussed. Preliminary evidence is presented, on small lattices, for center dominance in SU(3) lattice gauge theory.