Coulomb Energy, Vortices, and Confinement

TL;DR

This paper investigates the Coulomb energy of static quarks using lattice calculations, revealing a linear growth with distance and the critical role of center vortices in confinement.

Contribution

It provides the first detailed lattice calculation of Coulomb energy in Coulomb gauge and demonstrates the importance of center vortices in the confinement mechanism.

Findings

Coulomb energy grows linearly with quark separation.

The Coulomb string tension exceeds the asymptotic string tension.

Removing vortices causes the Coulomb string tension to vanish.

Abstract

We estimate the Coulomb energy of static quarks from a Monte Carlo calculation of the correlator of timelike link variables in Coulomb gauge. We find, in agreement with Cucchieri and Zwanziger, that this energy grows linearly with distance at large quark separations. The corresponding string tension, however, is several times greater than the accepted asymptotic string tension, indicating that a state containing only static sources, with no constituent gluons, is not the lowest energy flux tube state. The Coulomb energy is also measured on thermalized lattices with center vortices removed by the de Forcrand-D'Elia procedure. We find that when vortices are removed, the Coulomb string tension vanishes.