Non-perturbative formulation of the static color octet potential

TL;DR

This paper develops a gauge-invariant, non-perturbative approach to defining static color octet potentials in SU(N) gauge theories, supported by numerical simulations in 2+1 dimensions.

Contribution

It introduces a novel gauge-invariant method to construct static potentials in different color channels and provides numerical evidence for their behavior in SU(2) gauge theory.

Findings

Adjoint potential is repulsive at small distances.

At large separations, the adjoint potential becomes confining.

Lattice data matches perturbative predictions at small distances and high temperatures.

Abstract

By dressing Polyakov lines with appropriate functionals of the gauge fields, we construct observables describing a fundamental representation static quark-antiquark pair in the singlet, adjoint and average channels of SU(N) pure gauge theory. Each of the potentials represents a gauge invariant eigenvalue of the Hamiltonian. Numerical simulations are performed for SU(2) in 2+1 dimensions. The adjoint channel is found to be repulsive at small and confining at large separations, suggesting the existence of a metastable (N^2-1)-plet bound state. For small distances and temperatures above the deconfinement transition, the leading order perturbative prediction for the ratio of singlet and adjoint potentials is reproduced by the lattice data.