ar X iv : h ep - t h / 94 08 05 4 v 2 6 F eb 1 99 5 HD - THEP - 94 - 21 HIGH TEMPERATURE FIELD THEORY BEYOND PERTURBATION THEORY

For realistic values of the Higgs boson mass the high temperature electroweak phase transition cannot be described perturbatively. The symmetric phase is governed by a strongly interacting SU (2) gauge theory. Typical masses of excitations and scales of condensates are set by the " high temperature confinement scale " ≈ 0.2 T. For a Higgs boson mass around 100 GeV or above all aspects of the phase transition are highly nonperturbative. Near the critical temperature strong electroweak interactions are a dominant feature also in the phase with spontaneous symmetry breaking. Depending on the value of the Higgs boson mass the transition may be a first order phase transition or an analytical crossover. Phase transitions in the very early universe may be tumultuous periods out of ther-modynamic equilibrium. Some traces of such a transition may still be observable today, giving a hint on what happend shortly after the big bang. Remnants of the electroweak phase transition may help to understand the universe at the age of about 10 −12 s. One of the most prominent features of the standard model of electroweak interactions is spontaneous symmetry breaking. The masses of the gauge bosons and fermions are proportional to the vacuum expectation value of the Higgs doublet. According to the original argument of Kirzhnits and Linde 1 this expectation value vanishes at sufficiently high temperature and the electroweak symmetry is restored. Such high temperatures were presumably realized in the very early universe immediately after the big bang. As the universe cooled there must have been a phase transition from the the symmetric to the spontaneously broken phase of the standard model. This phase transition may have important consequences for our present universe, one example being the possible creation of the excess of matter compared to antimatter (baryon asymmetry) 2. The physical implications of the high temperature electroweak phase transition depend 1