Constraints on realistic Gauge-Higgs unified models

We investigate the general group structure of gauge-Higgs unified models. We find that a given embedding of the standard model gauge group will imply the presence of additional light vectors, except for a small set of special cases, which we determine; the arguments presented are independent of the compactification scheme. For this set of models we then find those that can both accommodate quarks and have a vanishing oblique $T$ parameter at tree level. We show that none of the resulting models can have $|s_{\mathrm{w}}|\sim 1/2$ (the sine of the weak-mixing angle) at tree level and briefly discuss possible solutions to this problem.