Infrared behavior of the Faddeev-Popov operator in Coulomb gauge QCD

TL;DR

This study investigates the eigenvalue distribution of the Faddeev-Popov operator in Coulomb gauge QCD through lattice simulations, revealing insights into confinement and deconfinement phases and their relation to the eigenvalue density.

Contribution

It provides the first lattice calculation of the Faddeev-Popov eigenvalue distribution in Coulomb gauge QCD across different phases, linking eigenvalue behavior to confinement criteria.

Findings

Eigenvalue density increases with volume in the confinement phase.

Eigenvalue behavior remains similar in the deconfinement phase.

Color-Coulomb potential remains unscreened in the deconfined phase.

Abstract

We calculate the eigenvalue distribution of the Faddeev-Popov operator in Coulomb gauge QCD using quenched SU(3) lattice simulation. In the confinement phase, the density of the low-lying eigenvalues increases with lattice volume, and the confinement criterion is satisfied. Moreover, even in the deconfinement phase, the behavior of the FP eigenvalue density is qualitatively the same as in the confinement phase. This is consistent with the fact that the color-Coulomb potential is not screened in the deconfined phase.