High Temperature 3D QCD: Dimensional Reduction at Work

TL;DR

This paper explores the behavior of three-dimensional SU(3) gauge theory at finite temperature, demonstrating that dimensional reduction accurately captures its properties down to relatively low temperatures and revealing unique screening phenomena.

Contribution

It provides an analytical derivation of the dimensionally reduced action and numerical analysis showing the effectiveness of dimensional reduction in 3D QCD at finite temperature.

Findings

Dimensional reduction works well down to 1.5 times the deconfinement temperature.

The color-averaged potential is dominated by a single state, not a pair of electric gluons.

The effective 2D theory accurately describes large-scale properties of 3D QCD at finite temperature.

Abstract

We investigate the three-dimensional SU(3) gauge theory at finite temperature in the framework of dimensional reduction. The large scale properties of this theory are expected to be conceptually more complicated than in four dimensions. The dimensionally reduced action is computed in closed analytical form. The resulting effective two-dimensional theory is studied numerically both in the electric and magnetic sector. We find that dimensional reduction works excellently down to temperatures of 1.5 times the deconfinement phase transition temperature and even on rather short length scales. We obtain strong evidence that for ${\rm QCD}_3$, even at high temperature the colour averaged potential is represented by the exchange of a single state, at variance with the usual Debye screening picture involving a pair of electric gluons.