Confinement in Three Dimensions and the Electroweak Phase Transition

The infrared behaviour of the standard model at finite temperature is determined by the confining phase of the SU(2)-Higgs model in three dimensions. Due to the Landau singularity of the three-dimensional gauge theory the perturbative treatment of the electroweak phase transition breaks down for Higgs masses above a critical mass $m_H^c$. Based on a renormalization group improved effective potential we find $m_H^c\sim$ 70 GeV. The scalar self-coupling has a Landau-type singularity also in the abelian U(1)-Higgs model, which leads to a breakdown of perturbation theory in the symmetric phase.