Aspects of Confinement in Coulomb Gauge

TL;DR

This paper explores confinement phenomena in Coulomb gauge through lattice comparisons, gluon contributions, and eigenvalue analysis, revealing insights into the ghost propagator, gluon-chain formation, and Gribov horizon effects.

Contribution

It introduces new results on confinement in Coulomb gauge, including lattice agreement with a Yang-Mills vacuum wavefunctional, gluon-chain formation evidence, and eigenvalue behavior near the Gribov horizon.

Findings

Lattice results agree with the proposed Yang-Mills vacuum wavefunctional.

Gluon contributions significantly improve quark-antiquark interaction modeling.

Eigenvalue analysis suggests the zero eigenvalue at the Gribov horizon may occur at non-zero momentum.

Abstract

I present some new results regarding confinement as it appears in Coulomb gauge. It is found that: i) a recently proposed Yang-Mills vacuum wavefunctional in temporal gauge and 2+1 dimensions yields a Coulomb-gauge ghost propagator and linear Coulomb potential in good agreement with lattice Monte Carlo results; ii) adding a few constituent gluons to heavy quark-antiquark states brings the interaction energy much closer to that of the static quark potential, and suggests the beginnings of gluon-chain formation at roughly one fermi; iii) a perturbative approach to Faddeev-Popov eigenvalues indicates that the zero eigenvalue at the Gribov horizon may occur either at, or away from, p=0, depending on the gauge choice and spacetime dimension. This last result may be relevant to the qualitatively different infrared behavior of the ghost propagator in Coulomb and Landau gauges.