Fermion mass hierarchies in low energy supergravity and superstring models

We investigate the problem of the fermion mass hierarchy in supergravity models with flat directions of the scalar potential associated with some gauge singlet moduli fields. The low-energy Yukawa couplings are nontrivial homogeneous functions of the moduli and a geometric constraint between them plays, in a large class of models, a crucial role in generating hierarchies. Explicit examples are given for no-scale type supergravity models. The Yukawa couplings are dynamical variables at low energy, to be determined by a minimization process which amounts to fixing ratios of the moduli fields. The Minimal Supersymmetric Standard Model (MSSM) is studied and the constraints needed on the parameters in order to have a top quark much heavier than the other fermions are worked out. The bottom mass is explicitly computed and shown to be compatible with the experimental data for a large region of the parameter space.