Coulomb gauge Gribov copies and the confining potential

We study the approach, initiated by Marinari et al., to the static interquark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant color charges. At larger separations Gribov copies obstruct the nonperturbative identification of individually gauge invariant color states. We demonstrate, for the first time, how gauge invariance can be maintained quite generally by averaging over Gribov copies. This allows us to extend the analysis of the Polyakov lines and the corresponding, gauge invariant quark-antiquark state to all distance scales. Using large scale lattice simulations, we show that this interpolating state possesses a good overlap with the ground state in the quark-antiquark sector and yields the full static interquark potential at all distances. A visual representation of the Gribov copies on the lattice is also presented.