The Fermion Generations Problem in the Gust in the Free World-Sheet Fermion Formulation

Abstract

In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the $SU(3{)}_H$-gauge family symmetry. We also develop some methods for building of corresponding string models. We explicitly construct GUST with gauge symmetry $G=SU(5)\times U(1)\times (SU(3)\times U(1){)}_H$ and $G=SO(10)\times (SU(3)\times U(1){)}_H$ or $E(6)\times SU(3{)}_H$ $\subset E(8)$ and consider the full massless spectrum for our string models. We consider for the observable gauge symmetry the diagonal subgroup $G^{symm}$ of the rank 16 group $G\times G$ $\subset SO(16)\times SO(16)$ or $\subset E(8)\times E(8)$. We discuss the possible fermion matter and Higgs sectors in these theories. We study renormalizable and nonrenormolizable contributions to the superpotential. There has to exist "superweak" light chiral matter ($m_H^f<M_W$) in GUST 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).

68 pages

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