Center vortices and the Gribov horizon

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.

Spectral decomposition of the ghost propagator and a necessary condition for confinement

“…(i) The massive level crossing makes the density of states, that is, the density of zero-modes, of the operator M diverge as compared to the density of zero modes of the Laplacian operator. This fits nicely with confinement scenario described in [20][21][22] where the divergence of the CCP is also understood as resulting from an enhanced density of states.…”

Coulomb flux tube on the lattice

“…In particular, the confining two point function is thought be due to a non-perturbative enhancement in the density of near-zero eigenvalues of the Faddeev-Popov operator, associated with the proximity of typical vacuum configurations to the Gribov horizon. It has been shown via lattice Monte Carlo simulations that removal of center vortices from thermalized lattice configurations sends this eigenvalue density back to the perturbative form [24], and the corresponding Coulomb string tension (along with the asymptotic string tension) vanishes upon vortex removal [10] (for recent developments in the vortex picture, see [25]). If center vortices or some other topological objects are responsible for the linearly rising Coulomb potential, it is probably necessary to also appeal to a topological mechanism in order to understand the formation of a Coulomb flux tube.…”

Effective Coulomb potential in SU(3) lattice Yang-Mills theory

“…A central element of the Gribov-Zwanziger confinement scenario in Coulomb gauge is the instantaneous colorCoulomb potential involving the Faddeev-Popov operator M (in Coulomb gauge) and the infrared spectral properties of the latter [5,6]. The expression V Coul ðx À yÞ ab ¼ hg 2 ½M À1 ðÀ4ÞM À1 ab ðx; yÞi…”

“…Recent lattice studies have shown, however, that the relation (4) is only a necessary [9] condition for confinement, and that the Coulomb potential can be linearly rising with spatial distance even in the deconfinement phase [6,10]. Using lattice techniques, a linearly rising Coulomb potential [9][10][11] and a connection between the center-vortex mechanism and the Gribov-Zwanziger scenario [5,12,13] have been observed. Furthermore, Greensite et al proposed [14] to use correlators of partial Polyakov loops to measure the Coulomb potential.…”