Thermal Phase Transition in the SO(5) x U(1) Gauge-Higgs Unification with 126GeV Higgs

We study the phase structure of the gauge theories in the space-time with one compact dimension, where the gauge symmetry can be broken by the Hosotani mechanism. As the extra dimension, we consider the SO(5) x U(1) gauge-Higgs unification in the Randall-Sundrum space-time which reproduce the 126 GeV Higgs mass. It is found that the thermal phase transition of the electroweak symmetry is almost second order and the critical temperature is around 160 GeV for z_L < 10^7 and n_F=3.