Gauge-Higgs unification with broken flavor symmetry

We study Gauge-Higgs unification model on the orbifold $S^{1}/Z_{2}$ based on the extended SM gauge group $G_{SM}^{ex}=SU(2)_{L} \times U(1)_{Y} \times SO(3)_{F}$. The group $SO(3)_{F}$ is treated as a chiral gauged flavour symmetry. Electroweak-, flavour- and Higgs interactions are unified in one single gauge group SU(7) which is broken again down to $G_{SM}^{ex}$ by orbifolding and imposing additional boundary conditions. The compactification scale is O(1) TeV. The orbifold $S^{1}/Z_{2}$ is put on a lattice. This setting gives a staring point for RG-transformations. As a result the bulk is integrated out and the extra dimension consist of only two points: the orbifold fixed points. Parallel transporters (PT) in the extra dimension become nonunitary as a result of the blockspin transformations. In addition, a Higgs potential emerges naturally. The PTs can be written as a product $e^{A_{y}} e^{\eta} e^{A_{y}}$ of unitary factors $e^{A_{y}}$ and a selfadjoint factor $e^{\eta}$. The reduction $48 \to 35 + 6 + \bar{6} + 1$ of the adjoint reps of SU(7) with respect to $SU(6) \supset G_{SM}^{ex}$ leads to three $SU(2)_{L}$ Higgs doublets: one for each flavour. Their zero modes serve as a substitute for the SM Higgs. When $G_{SM}^{ex}$ is spontaneously broken down to $U(1)_{em}$, an exponential gauge boson mass splitting occurs naturally. This breaking leads to $SO(3)_{F}$ flavour gauge boson masses much above the compactification scale. Thus tree-level FCNC are naturally suppressed. Making some simplifying assumptions we also calculate fermion masses and CKM mixing angles. As for the gauge bosons an exponential fermion mass splitting occurs naturally. The model predicts a large Higgs sector consisting of 30 Higgs particles and in its simplest form the weak mixing angle $\theta=0.125$.