SU(N)Supersymmetric Grand Unified Theories: Natural Projection to Low Energies

We argue that the gauge hierarchy phenomenon, properly interpreted in terms of the natural missing vacuum expectation value solution for the adjoint scalar in general $\mathrm{SU}\left(N\right)$ supersymmetric grand unified theory, may give insight into both of the basic features of low-energy physics accommodated in the standard model which are some strict color-flavor (or color-family) interrelation and the $\mathrm{SU}\left(2\right)$ symmetry structure of weak interactions. There, apart from the ordinary triple matter of the minimal supersymmetric standard model, just three families of the pseudo-Goldstone states are predicted at a TeV scale in the minimal $\mathrm{SU}\left(8\right)$ theory.