Families from supergroups and predictions for leptonic CP violation

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M |N ), can give interesting anomaly-free sets of fermion representations of SU(M ) × SU(N ) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.