The gauge coupling evolutions of an SU(8) theory with the maximally symmetry breaking pattern

We study the renormalizable group equations (RGEs) of the extended strong and weak gauge couplings in an SU(8) theory, where three-generational SM fermions are non-trivially embedded. This framework was previously found to generate the observed SM quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern through its maximally breaking pattern. The field theoretical two-loop RGEs can not achieve the gauge coupling unification with the minimal setup, unless additional adjoint Higgs fields as well as the gravity-induced $d=5$ term to the SU(8) field strength term are included.