Abstract
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 ) × U ( 1 ) χ × SU ( 4 ) ⊥ in which U ( 1 ) χ plays the role of a generalised matter parity. We present an example which, after imposing a Z 2 monodromy, has a U ( 1 ) ⊥ 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 ) × SU ( 5 ) ⊥ with a U ( 1 ) ⊥ 3 family symmetry after imposing a Z 2 monodromy.
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