Confinement in 3D Gluodynamics as a 2D Critical Phenomenon

TL;DR

This paper explores how confinement in 3D gluodynamics with one compactified spatial dimension can be understood as a 2D critical phenomenon, specifically a Kosterlitz-Thouless transition driven by vortex excitations.

Contribution

It demonstrates that the confinement transition in 3D gluodynamics maps onto a 2D non-linear sigma-model, revealing a topological vortex mechanism analogous to the Kosterlitz-Thouless transition.

Findings

Confinement order parameters behave as in a 2D sigma-model in the large L limit.

Vortex-like excitations induce a Kosterlitz-Thouless phase transition.

The phase transition is linked to the confinement-deconfinement transition in 3D gluodynamics.

Abstract

Gluodynamics in 3D spacetime with one spatial direction compactified into a circle of length $L$ is studied. The confinement order parameters, such as the Polyakov loops, are analyzed in both the limits $L \to 0$ and $L \to \infty$. In the latter limit the behavior of the confinement order parameters is shown to be described by a 2D non-linear sigma-model on the compact coset space $G/ad G$, where $G$ is the gauge group and $ad G$ its adjoint action on $G$. Topological vortex-like excitations of the compact field variable cause a Kosterlitz-Thouless phase transition which is argued to be associated with the confinement phase transition in the 3D gluodynamics.