Effective confinement theory from Abelian variables in SU(3) gauge theory

TL;DR

This paper develops an effective confinement theory for SU(3) gauge theory using Abelian variables and the Julia-Toulouse approach, revealing a confining potential with short-range and long-range components.

Contribution

It introduces a gauge-invariant method to derive an effective confinement theory from Abelian variables in SU(3) gauge theory without gauge fixing.

Findings

The effective theory exhibits a Yukawa potential at short distances.

A linear confining potential dominates at large distances.

The approach is compatible with Elitzur's theorem.

Abstract

In this Letter we use the Julia-Toulouse approach for condensation of defects in order to obtain an effective confinement theory for external chromoelectric probe charges in SU(3) gauge theory in the regime with condensed chromomagnetic monopoles. We use the Cho decomposition of the non-Abelian connection in order to reveal the Abelian sector of the non-Abelian gauge theory and the associated topological defects (monopoles) without resorting to any gauge fixing procedure. Using only the Abelian sector of the theory, we construct a hydrodynamic effective theory for the regime with condensed defects in such a way that it is compatible with the Elitzur's theorem. The resulting effective theory describes the interaction between external chromoelectric probe charges displaying a short-range Yukawa interaction plus a linear confining term that governs the long distance physics.