Coulomb Confinement from the Yang-Mills Vacuum State in 2+1 Dimensions

TL;DR

This paper investigates the Coulomb gauge ghost propagator and color-Coulomb potential in 2+1 dimensional Yang-Mills theory using a proposed vacuum wavefunctional, comparing results with Monte Carlo simulations and analyzing the effects of low eigenvalue configurations.

Contribution

It introduces a new approach to compute the Coulomb gauge quantities from a specific Yang-Mills vacuum wavefunctional in 2+1 dimensions and compares these with standard Monte Carlo results.

Findings

The ghost propagator results agree well with Monte Carlo data.

The color-Coulomb potential exhibits linear rise at large distances.

Low eigenvalue configurations significantly affect the potential's statistical fluctuations.

Abstract

The Coulomb-gauge ghost propagator, and the color-Coulomb potential, are computed in an ensemble of configurations derived from our recently proposed Yang-Mills vacuum wavefunctional in 2+1 dimensions. The results are compared to the corresponding values obtained by standard Monte Carlo simulations in three Euclidean dimensions. The agreement is quite striking for the Coulomb-gauge ghost propagator. The color-Coulomb potential rises linearly at large distances, but its determination suffers from rather large statistical fluctuations, due to configurations with very low values of $\mu_0$, the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. However, if one imposes cuts on the data, effectively leaving out configurations with very low $\mu_0$, the agreement of the potential in both sets of configurations is again satisfactory, although the errorbars grow systematically as the cutoff is eliminated.