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 $T^2/Z_2$ 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, $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$, 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.