The electroweak phase transition on orbifolds with gauge-Higgs unification

The dynamics of five dimensional Wilson line phases at finite temperature is studied in the one-loop approximation. We show that at temperatures of order $T\sim 1/L$, where $L$ is the length of the compact space, the gauge symmetry is always restored and the electroweak phase transition appears to be of first order. Particular attention is devoted to the study of a recently proposed five dimensional orbifold model (on $S^1/\Z_2$) where the Wilson line phase is identified with the Higgs field (gauge-Higgs unification). Interestingly enough, an estimate of the leading higher-loop ``daisy'' (or ``ring'') diagram contributions to the effective potential in a simple five dimensional model, seems to suggest that the electroweak phase transition can be studied in perturbation theory even for Higgs masses above the current experimental limit of 114 GeV. The transition is still of first order for such values of the Higgs mass. If large localized gauge kinetic terms are present, the transition might be strong enough to give baryogenesis at the electroweak transition.