Realization of dimensional reduction at high temperature

Abstract

Renormalizable four-dimensional field theories reduce at high temperature to effective three-dimensional field models with generically nonlocal interactions induced by the thermal degrees of freedom. Reduction to a local and renormalizable effective model is analyzed here for the example ofSU(N _c ) lattice gauge theory by means of perturbation theory. The infrared problems are cured by applying the coupled large volume and small coupling expansion. ForSU(2) it is shown to the lower orders in this expansion that in the temperature rangeT≧3T _c dimensional reduction applies, where we consider the following observables: thermal Polyakov line correlations, out of which the interquark potential is derived, and spatial Wilson loops. We also propose an alternative description, in which the effective theory is a gauge theory that lives on a lattice with one time slice and a least number of effective vertices.