Fermion masses and mixings in a flavour symmetric GUT

We describe a supersymmetric Grand Unified Theory based on the gauge group SU(5), or SO(10), invariant under the interchange of any SU(5), or SO(10), with each family multiplet transforming non trivially under one different individual group factor. A realistic pattern of fermion masses and mixings is obtained as a result of an appropriate choice out of the many possible discretely degenerate vacua of the theory. In the SO(10) case, we predict the three neutrino masses in terms of an overall scale and, within factors of order unity, their mixing angles. A νe-νμ oscillation is suggested as a solution of the solar neutrino problem, implying a visible νμ-ντ oscillation in the forthcoming experiments. Grand unified theories of this type could be obtainable in a string theory framework. ∗ Permanent address: Institute of Physics, Georgian Academy of Sciences, 380077 Tbilisi, Georgia.