Supersymmetric three family chiral SU(6) grand unification model from F-theory

We obtain a supersymmetric three family chiral SU(6) grand unification model with the global family symmetry SU(3)_family from the use of F-theory. This model has nice features, for instance, all the fermion masses are reasonably generated and result in only one pair of Higgs doublets, giving the doublet-triplet splitting from the family symmetry SU(3)_family. The proton hexality is also realized toward the proton stability problem. The model also has a room to fit the three gauge couplings using the F-theory flux idea and we obtain the upper bound of proton lifetime in the 1036^-37yr region.