Gauge-Fermion unification and flavour symmetry

After we study the 6-dimensional = (1,1) supersymmetry breaking and R symmetry breaking on M4 × T2/Zn, we construct two = (1,1) supersymmetric E6 models on M4 × T2/Z3 where E6 is broken down to SO(10) × U(1)X by orbifold projection. In Model I, three families of the Standard Model fermions arise from the zero modes of bulk vector multiplet, and the R symmetry U(1)FI × SU(2)4− can be considered as flavour symmetry. This may explain why there are three families of fermions in the nature. In Model II, the first two families come from the zero modes of bulk vector multiplet, and the flavour symmetry is similar. In these models, the anomalies can be cancelled, and we have very good fits to the SM fermion masses and mixings. We also comment on the = (1,1) supersymmetric E6 models on M4 × T2/Z4 and M4 × T2/Z6, SU(9) models on M4 × T2/Z3, and SU(8) models on T2 orbifolds.

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