Fermion mass hierarchy in six-dimensional SO(10) grand unified theory on a T2/Z2 orbifold

We suggest a simple supersymmetric SO(10) grand unified theory in 6 dimensions which produces the suitable fermion mass hierarchies. The 5th- and 6th-dimensional coordinates are compactified on a T2/Z2 orbifold. The gauge and Higgs fields propagate in 6 dimensions while ordinal chiral matter fields are localized in 4 dimensions. The orbifolding and boundary conditions realize the gauge symmetry reduction, SU(3)C×SU(2)L×U(1)Y×U(1)X, and the triplet–doublet mass splitting. We introduce extra three sets of vector-like heavy fields: two sets propagate in 6 dimensions and chiral fields which couple to them are defined as the 1st generation, and one set propagates in 5 dimensions and chiral fields which couple to them are defined as the 2nd generation. The suitable fermion mass hierarchies are generated by integrating out these vector-like heavy fields.