Confinement in 3D Gluodynamics as a 2D Critical Phenomenon

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 $G/adG$, where $G$ is the gauge group and $adG$ 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.

4 pages, LaTeX. Talk presented at the 2nd Int. Conf. on Quark Confinement and the Hadron Spectrum in Como (Italy)