Critical bubbles and fluctuations at the electroweak phase transition

We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field \varphi. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g_3(T)^2 in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(\varphi) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small \varphi values increasing with the Higgs mass m_H. Taking a functional S_z[\varphi] with constant Z(\varphi)=z instead of the full non-local effective action in some neighborhood of the saddlepoint we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.