Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang-Mills theory

TL;DR

This paper investigates how low-lying eigenmodes of the Faddeev-Popov ghost operator influence the confining color-Coulomb potential in SU(3) lattice Yang-Mills theory, highlighting the importance of Gribov copies and spectral sums.

Contribution

It demonstrates the significant role of near-zero FP eigenmodes in the color-Coulomb potential and analyzes the impact of Gribov copies on eigenvalues and confinement.

Findings

Lowest eigenvalue vanishes faster in the thermodynamic limit than in Landau gauge.

Near-zero FP eigenmodes dominate the large-distance color-Coulomb potential.

The lowest eigenmode contributes substantially to the string tension.

Abstract

We discuss the essential role of the low-lying eigenmodes of the Faddeev-Popov (FP) ghost operator on the confining color-Coulomb potential using SU(3) quenched lattice simulations in the Coulomb gauge. The color-Coulomb potential is expressed as a spectral sum of the FP ghost operator and has been explored by partially summing the FP eigenmodes. We take into account the Gribov copy effects that have a great impact on the FP eigenvalues and the color-Coulomb potential. We observe that the lowest eigenvalue vanishes in the thermodynamic limit much faster than that in the Landau gauge. The color-Coulomb potential at large distances is governed by the near-zero FP eigenmodes; in particular, the lowest one accounts for a substantial portion of the color-Coulomb string tension comparable to the Wilson string tension.