The effective Coulomb potential in SU(3) lattice Yang-Mills theory

TL;DR

This paper investigates the infrared behavior of the effective Coulomb potential in SU(3) lattice Yang-Mills theory, revealing scaling violations and Gribov copy dependence, and providing bounds consistent with theoretical inequalities.

Contribution

It presents the first detailed lattice study of the Coulomb potential's infrared behavior in SU(3) Yang-Mills theory, highlighting finite-volume effects and Gribov copy issues.

Findings

Finite-volume effects are minimal in the Coulomb potential.

Strong dependence on Gribov copy choice is observed.

Bounds on Coulomb string tension agree with Zwanziger's inequality.

Abstract

We study the infrared behavior of the effective Coulomb potential in lattice SU(3) Yang-Mills theory in the Coulomb gauge. We use lattices up to a size of 48^4 and three values of the inverse coupling, beta=5.8, 6.0 and 6.2. While finite-volume effects are hardly visible in the effective Coulomb potential, scaling violations and a strong dependence on the choice of Gribov copy are observed. We obtain bounds for the Coulomb string tension that are in agreement with Zwanziger's inequality relating the Coulomb string tension to the Wilson string tension.