The QCD vacuum wave functional and confinement in Coulomb gauge

TL;DR

This paper compares the Coulomb-gauge ghost propagator and color-Coulomb potential in two lattice gauge-field ensembles, revealing strong agreement in ghost propagators but some differences in potentials due to rare configurations.

Contribution

It provides a comparative analysis of the ghost propagator and Coulomb potential in different lattice ensembles, connecting a proposed vacuum wave functional with Monte Carlo simulations.

Findings

Remarkable agreement in ghost propagators across ensembles

Differences in potentials due to rare low eigenvalue configurations

Applying cuts on exceptional configurations improves potential agreement

Abstract

We report results on the Coulomb-gauge ghost propagator and the color-Coulomb potential computed in two lattice gauge-field ensembles: (1) configurations derived from our recently proposed Yang-Mills vacuum wave functional in 2+1 dimensions, and (2) lattices generated by Monte Carlo simulations of the three-dimensional Euclidean SU(2) lattice gauge theory with the Wilson action. We observe remarkable agreement between the ghost propagators in both ensembles, but some differences in the potentials. Those originate from rare configurations with very small values of the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. If the same cuts on such exceptional configurations are applied in both ensembles, then the color-Coulomb potentials are also in reasonably good agreement.