The effective potential and universality in GUT inspired gauge-Higgs unification

The effective potential for the Aharonov-Bohm phase $\theta_H$ in the fifth dimension in GUT inspired $SO(5)\times U(1) \times SU(3)$ gauge-Higgs unification is evaluated to show that dynamical electroweak symmetry breaking takes place with $\theta_H \not= 0$, the 4D Higgs boson mass 125$\,$GeV being generated at the quantum level. The cubic and quartic self-couplings $(\lambda_3, \lambda_4)$ of the Higgs boson are found to satisfy universal relations, i.e. they are determined, to high accuracy, solely by $\theta_H$, irrespective of values of other parameters in the model. For $\theta_H=0.1$ ($0.15$), $\lambda_3$ and $\lambda_4$ are smaller than those in the standard model by 7.7% (8.1%) and 30% (32%), respectively.