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We discuss a possibility whether a model of grand gauge-Higgs unification incorporating family unification in higher dimensions can be constructed. We first extend a five-dimensional SU(6) grand gauge-Higgs unification model to a five-dimensional SU(7) grand gauge-Higgs unification model compactified on an orbifold S1/Z2 to obtain three generations of quarks and leptons after symmetry breaking of the larger family unified gauge group. A prescription of constructing a six-dimensional SU(N) grand gauge-Higgs unification model including a five-dimensional SU(7) grand gauge-Higgs unification after compactifying the sixth dimension on an orbifold S1/Z2 is given. We find a six-dimensional SU(14) grand gauge-Higgs unification model with a set of representations containing three generations of quarks and leptons. Published by the American Physical Society 2024
Maru et al. (Fri,) studied this question.