Center Vortices and the Gribov Horizon

TL;DR

This paper explores the connection between center vortices, the Gribov horizon, and the density of near-zero Faddeev-Popov eigenmodes, revealing their role in confinement and gauge configuration space geometry.

Contribution

It demonstrates the link between center vortex percolation, eigenvalue density enhancement, and the Gribov horizon's structure in gauge theories.

Findings

Enhanced eigenvalue density is tied to percolating vortices.

Thin vortices are located at singularities on the Gribov horizon.

The Gribov region is a convex manifold in configuration space.

Abstract

We show how the infinite color-Coulomb energy of color-charged states is related to enhanced density of near-zero modes of the Faddeev-Popov operator, and calculate this density numerically for both pure Yang-Mills and gauge-Higgs systems 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 presence of percolating center vortex configurations, and that this property disappears when center vortices are either removed from the lattice configurations, or cease to percolate. We further demonstrate that thin center vortices have a special geometrical status in gauge-field configuration space: Thin vortices are located at conical or wedge singularities on the Gribov horizon. We show that the Gribov region is itself a convex manifold in lattice configuration space. The Coulomb gauge condition also has a special status; it is shown to be an attractive fixed point of a more general gauge condition, interpolating between the Coulomb and Landau gauges.