THE FERMION GENERATION PROBLEM IN THE GUST’S OF THE FREE WORLD SHEET FERMION FORMULATION

Abstract

In the framework of the four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU (3) H gauge family symmetry, and develop some methods for building corresponding string models. We explicitly construct GUST’s with gauge symmetry G= SU (5)× U (1) × [ SU (3)× U (1)] H and G= SO (10)×[ SU (3)× U (1)] H ⊂ SO (16) or E(6)× SU (3) H ⊂ E(8), and consider the full massless spectrum for our string models. As the GUST’s originating from level 1 Kac–Moody algebra (KMA) contain only low-dimensional representations, we consider for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO (16)× SO (16) or ⊂ E(8)×E(8). We discuss the possible fermion matter and Higgs sectors in these theories. There has to exist “superweak” light chiral matter [Formula: see text] in the GUST’s under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the SU (3) H family gauge symmetry (some TeV).