Family symmetries in F-theory GUTs

We discuss F-theory SU(5) GUTs in which some or all of the quark and lepton families are assigned to different curves and family symmetry enforces a leading order rank one structure of the Yukawa matrices. We consider two possibilities for the suppression of baryon and lepton number violation. The first is based on Flipped SU (5) with gauge group SU(5) x U(1)(x) x SU(4)perpendicular to in which U(I)(x) plays the role of a generalised matter parity. We present an example which, after imposing a Z(2) monodromy, has a U(1)(perpendicular to)(2) family symmetry. Even in the absence of flux, spontaneous breaking of the family symmetry leads to viable quark, charged lepton and neutrino masses and mixing. The second possibility has an R-parity associated with the symmetry of the underlying compactification manifold and the flux. We construct an example of a model with viable masses and mixing angles based on the gauge group SU(5) x SU(5)1 with a U(1)-(3)(perpendicular to) family symmetry after imposing a Z(2) monodromy. (C) 2010 Elsevier B.V. All rights reserved.