5-Dimensional Difficulties of Gauge-Higgs Unifications

Abstract

We consider 5 dimensional gauge theories where the 5th direction is compactified on the orbifold S^1/Z_2, and where the 5th components of the gauge bosons play the role of the Standard Model Higgs boson (gauge-Higgs unification). The gauge symmetry breaking is realized through the appropriate orbifold boundary conditions and through the Hosotani mechanism. We show that for {\em any such theory} the assumption that the low-energy vector-boson spectrum consists of the W^\pm, Z and \gamma only, is inconsistent with the experimental requirements \sin^2\theta_W\simeq 1/4 and \rho\equiv m_W^2/(m_Z^2\cos^2\theta_w)=1.