26 research outputs found
Matter wave functions and Yukawa couplings in F-theory Grand Unification
We study the local structure of zero mode wave functions of chiral matter
fields in F-theory unification. We solve the differential equations for the
zero modes derived from local Higgsing in the 8-dimensional parent action of
F-theory 7-branes. The solutions are found as expansions both in powers and
derivatives of the magnetic fluxes. Yukawa couplings are given by an overlap
integral of the three wave functions involved in the interaction and can be
calculated analytically. We provide explicit expressions for these Yukawas to
second order both in the flux and derivative expansions and discuss the effect
of higher order terms. We explicitly describe the dependence of the couplings
on the U(1) charges of the relevant fields, appropriately taking into account
their normalization. A hierarchical Yukawa structure is naturally obtained. The
application of our results to the understanding of the observed hierarchies of
quarks and leptons is discussed.Comment: Latex, 51 pages, 4 figures, typos corrected, note adde
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