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Yukawa Structure from U(1) Fluxes in F-theory Grand Unification
In F-theory GUT constructions Yukawa couplings necessarily take place at the
intersection of three matter curves. For generic geometric configurations this
gives rise to problematic Yukawa couplings unable to reproduce the observed
hierarchies. We point out that if the U(1)_{B-L}/U(1)_Y flux breaking the
SO(10)/SU(5) GUT symmetry is allowed to go through pairs of matter curves with
the same GUT representation, the quark/lepton content is redistributed in such
a way that all quark and leptons are allowed to have hierarchical Yukawas. This
reshuffling of fermions is quite unique and is particularly elegant for the
case of three generations and SO(10). Specific local F-theory models with
SO(10) or SU(5) living on a del Pezzo surface with appropriate bundles and just
the massless content of the MSSM are described. We point out that the smallness
of the 3rd generation quark mixing predicted by this scheme (together with
gauge coupling unification) could constitute a first hint of an underlying
F-theory grand unification.Comment: 31 pages, 3 figures, Latex fil