SU(7) Grand Gauge-Higgs Unification

We propose a model of six dimensional $SU(7)$ grand gauge-Higgs unification compactified on $S^1\mathrm{/}{Z}_2\mathrm{/}times{S}^1\mathrm{/}{Z}_2$, which is a six dimensional extension of five dimensional $SU(4)$ gauge-Higgs unification predicting the weak mixing angle $\mathrm{/}si{n}^2\mathrm{/}thet{a}_W=1\mathrm{/}4$ at the compactification scale. We investigate whether the correct pattern of electroweak symmetry breaking is realized in our model. We find some solutions providing the electroweak symmetry breaking and a realistic Higgs mass. Corresponding to each solution, the compactification scale of the fifth dimension is predicted. Furthermore, we evaluate the weak mixing angle at the weak scale by using one-loop renormalization group equation and find it to be in good agreement with the experimental data.