Flavor hierarchy from F-theory

It has recently been shown that F-theory based constructions provide a potentially promising avenue for engineering GUT models which descend to the MSSM. In this Note we show that in the presence of background fluxes, these models automatically achieve hierarchical Yukawa matrices in the quark and lepton sectors. At leading order, the existence of a U(l) symmetry which is related to phase rotations of the internal holomorphic coordinates at the brane intersection point leads to rank one Yukawa matrices. Subleading corrections to the internal wave functions from variations in the background fluxes generate small violations of this U(1), leading to hierarchical Yukawa structures reminiscent of the Froggatt Nielsen mechanism. The expansion parameter for this perturbation is in terms of root alpha(GUT). Moreover, we naturally obtain a hierarchical CKM matrix with V-12 similar to V-21 similar to epsilon, V-23 similar to V-32 similar to epsilon(2), V-13 similar to V-31 similar to epsilon(3), where epsilon similar to root alpha GUT, in excellent agreement with observation. (C) 2010 Published by Elsevier By.