Dimensional reduction at high temperature revisited

Abstract

We give a perturbative analysis of dimensional reduction in the infinite-temperature limit of thermal field theory in the imaginary-time formalism. In analogy with the ordinary (Appelquist-Carazzone) decoupling theorem, we seek a class of renormalization schemes in which the heavy (non-static) modes decouple. This class turns out to consist of temperature-dependent schemes, so that the appropriate context to study dimensional reduction at high T is seen to be the finite-temperature renormalization group. As a corollary, it follows that dimensional reduction to all orders occurs only in exceptional cases; in scalar field theories and QCD such a reduction is valid only up to a given (low) order of normalization-group improved perturbation theory.