Color confinement in Coulomb gauge QCD

TL;DR

This paper demonstrates that in Coulomb gauge QCD, the heavy quark potential exhibits a linearly rising behavior at large distances, indicating confinement, and this persists even in the deconfinement phase, with results consistent across SU(2) and SU(3).

Contribution

It provides lattice simulation evidence that the Coulomb gauge heavy quark potential is confining and exceeds the Wilson loop tension, supporting Zwanziger's inequality and extending previous SU(2) findings to SU(3).

Findings

Coulomb heavy quark potential rises linearly at large distances.

Coulomb string tension exceeds Wilson loop string tension.

Confinement persists even in deconfinement phase.

Abstract

We study the long-range behavior of the heavy quark potential in Coulomb gauge using a quenched SU(3) lattice gauge simulation with partial-length Polyakov line correlators. We show that the Coulomb heavy quark potential associated with the instantaneous part of gluon propagators in Coulomb gauge, presents a linearly rising behavior at large distances, and the resulting Coulomb string tension is greater than the Wilson loop string tension, which can be explained by Zwanziger's inequality. The linearly rising behavior of the Coulomb heavy quark potential persists even in the deconfinement phase. The heavy quark potential in Lorentz gauge shows completely different behavior than that in Coulomb gauge. Our SU(3) result, i.e., the Coulomb heavy quark potential is confining, qualitatively agrees with that of the SU(2) analysis carried out by Greensite, Olejnik and Zwanziger.