Confinement in 3D Gluodynamics as a 2D Critical Phenomenon

Details Confinement in 3D Gluodynamics as a 2D Critical Phenomenon Confinement in 3D Gluodynamics as a 2D Critical Phenomenon

1997-01-03

arxiv.org/abs/hep-th/9701006v1

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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.

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