Coulomb gauge Gribov copies and the confining potential

Abstract

We study the approach, initiated by Marinari et al., to the static inter-quark 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 colour charges. At larger separations Gribov copies obstruct the non-perturbative identification of individually gauge invariant colour 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 inter-quark potential at all distances. A visual representation of the Gribov copies on the lattice is also presented.

arXiv comment22 pages, 9 figures, v2: minor changes, references added

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Cited by in corpus (9)

• Static quark-antiquark potential in the quark-gluon plasma from lattice QCD
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• Symmetry breaking, conformal geometry and gauge invariance
• More on the properties of the first Gribov region in Landau gauge
• Is the ground state of Yang-Mills theory Coulombic?
• Probing the ground state in gauge theories
• The ice-limit of Coulomb gauge Yang-Mills theory
• The factorisation of glue and mass terms in SU(N) gauge theories
• Unphysical properties of the static quark-antiquark four-point correlator in Landau gauge