Center vortices and the Gribov horizon

We show how the infinite color-Coulomb energy of color-charged states isrelated to enhanced density of near-zero modes of the Faddeev-Popov operator,and calculate this density numerically for both pure Yang-Mills and gauge-Higgssystems at zero temperature, and for pure gauge theory in the deconfined phase.We find that the enhancement of the eigenvalue density is tied to the presenceof percolating center vortex configurations, and that this property disappearswhen center vortices are either removed from the lattice configurations, orcease to percolate. We further demonstrate that thin center vortices have aspecial geometrical status in gauge-field configuration space: Thin vorticesare located at conical or wedge singularities on the Gribov horizon. We showthat the Gribov region is itself a convex manifold in lattice configurationspace. The Coulomb gauge condition also has a special status; it is shown to bean attractive fixed point of a more general gauge condition, interpolatingbetween the Coulomb and Landau gauges.Comment: 19 pages, 17 EPS figures, RevTeX4; v2: added references, corrected caption of fig. 11; v3: new data for higher couplings, clarifications on color-Coulomb potential in deconfined phase, version to appear in JHE