M-Theory Phenomenology and See-Saw Mechanisms

A version of M-theory phenomenology is proposed in which the symmetry is based on the group $SO(10) \times SO(10) \times SO(10) \times U(1) \times U(1)$. Each SO(10) group acts on a single generation. The $U(1) \times U(1)$ is regarded as the hidden sector symmetry group. The supersymmetry is broken in the hidden sector by the Fayet-Iliopoulos $D$-term for each group. The $D$-term is needed also to circumvent the powerful non-renormalization theorem since the $SO(10) \times SO(10) \times SO(10)$ is broken down to the usual SO(10) by the pair condensation of certain messenger sector multiplets. The exchange of U(1) gauge bosons gives an attractive force for the pair to be created and condensed. The off-diagonal mass matrix elements among the generations in these messenger sector multiplets are the source of the flavor dynamics including the CP violation. The pair condensation of another multiplet in the messenger sector leads to the doublet-triplet splitting. The SO(10) decuplet Higgs couples only to one of the generations. The other couplings should, therefore, be calculated as higher order corrections. We present our preliminary results on the calculation of the mass matrices and the mixing angles for leptons and quarks in this model.