Confining Strings in the Abelian-Projected SU(3)-Gluodynamics

TL;DR

This paper constructs a string representation of the Wilson loop in 3D Abelian-projected SU(3)-gluodynamics, demonstrating confinement through a dilute monopole gas approximation, which simplifies the analysis compared to monopole condensation.

Contribution

It introduces a novel approach to represent the Wilson loop via an effective multivalued potential, relaxing the monopole condensation requirement.

Findings

Wilson loop expressed through monopole densities

Confinement demonstrated in dilute monopole gas approximation

Effective potential approach simplifies analysis

Abstract

String representation of the Wilson loop in 3D Abelian-projected SU(3)-gluodynamics is constructed in the approximation that Abelian-projected monopoles form a gas. Such an assumption is much weaker than the standard one, demanding the monopole condensation. It is demonstrated that the summation over world sheets, bounded by the contour of the Wilson loop, is realized by the summation over branches of a certain effective multivalued potential of the monopole densities. Finally, by virtue of the so-constructed representation of the Wilson loop in terms of the monopole densities, this quantity is evaluated in the approximation of a dilute monopole gas, which makes confinement in the model under study manifest.