GRAND UNIFIED STRING THEORIES WITH SU(3) GAUGE FAMILY SYMMETRY

In the framework of four dimensional heterotic superstring with free fermions we investigate the rank eight Grand Unified String Theories (GUST) which contain the SU(3)H-gauge family symmetry. We explicitly construct GUSTs with gauge symmetry G = SU(5) x U(1) x (SU(3) x U(1))H subset-of SO(16) subset-of E(8) in free complex fermion formulation. We solve the problem of the GUST symmetry breaking taking for the observable gauge symmetry the diagonal subgroup G(sym) of rank 16 group G x G subset-of SO(16) x SO(16) subset-of E(8) x E(8). In this approach the observed electromagnetic charge Q(em) can be viewed as a sum of two Q1- and Q2-charges of each G-group. In this case the model spectrum does not contain particles with exotic fractional charges.