Confinement in a three-dimensional Yang-Mills theory

TL;DR

This paper analytically derives the string tension and confining potential in a three-dimensional Yang-Mills theory from classical solutions, achieving excellent agreement with lattice results and previous theoretical models.

Contribution

It provides an analytical derivation of the string tension and potential in 3D Yang-Mills theory directly from classical solutions, justifying a previously arbitrary numerical factor.

Findings

String tension matches lattice results within 1%.

Potential is consistent with a marginally confining theory.

Derivation confirms the numerical factor from classical solutions.

Abstract

We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.