Coulomb confinement from the Yang-Mills vacuum state in 2+1 dimensions

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 wave functional 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 μ0, 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 μ0, the agreement of the potential in both sets of configurations is again satisfactory, although the error bars grow systematically as the cutoff is eliminated.