The fermion generations phenomenology in Grand Unified Superstring Theories (GUSTs)

In the framework of the four dimensional heterotic superstring with free world-sheet fermions and using all constraints due to the conformal and superconformal symmetries (Virasoro and super-Virasoro algebras), the Kac-Moody current algebra, the global reparametrization (modular) invariance and the autoduality of the fermion charge lattice we study the rank eight/sixteen Grand Unified String Theories (GUST) which contain the non-abelian gauge family symmetry. We discuss the possible fermion matter and Higgs sectors in some GUST theories. We study string amplitudes and for one realistic model we explicitly calculate the renormalizable (N=3) and nonrenormolizable (N=4,5,6) contributions to the superpotential.