Fermion Mass Hierarchy in Six Dimensional SO ( 10 ) Grand Unified Theory on a T

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 T 2 /Z 2 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.