Effective potential of Higgs field in warped gauge-Higgs unification

Gauge-Higgs unification is one of the influential scenarios for solving the hierarchy problem in the Standard Model. Recently, the scenario on the warped background attracts much attention owing to a large possibility to construct a realistic model naturally in this framework. It is, however; well known that the effective potential for the Higgs field, which is the most important prediction of the scenario, is not easy to calculate on the warped background, because masses of Kaluza-Klein particles are not obtained analytically. In this article; we derive useful formulae for the effective potential. The formulae allow its to calculate Higgs mass easily, and thus to construct a realistic model in the gauge-Higgs unification scenario on the warped background. Using the obtained formulae, we calculate the contributions of bulk fermions with several boundary conditions. We also show that bulk fermions that have boundary conditions prohibited in the orbifold picture do not contribute to the effective potential. The formulae allow us to examine the infrared behavior of the effective potential, and we investigate the Gauge-Higgs condition that the effective theory should satisfy.