Orbifold family unification using vectorlike representation on six dimensions

In orbifold family unification on the basis of SU(N) gauge theory on the six-dimensional space-time M-4 x T-2/Z(m) (m = 2, 3, 4, 6), enormous numbers of models with three families of the standard model matter multiplets are derived from a massless Dirac fermion in a vectorlike representation [N, 3] + [N, N - 3] of SU(N) (N = 8, 9). They contain models with three or more than three neutrino singlets and without any non-Abelian continuous flavor gauge symmetries. The relationship between flavor numbers from a fermion in [N, N - k] and those from a fermion in [N, k] are studied from the viewpoint of charge conjugation.