Flavor hierarchy from F-theory Original Research Article

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 image 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 image, leading to hierarchical Yukawa structures reminiscent of the Froggatt–Nielsen mechanism. The expansion parameter for this perturbation is in terms of image. Moreover, we naturally obtain a hierarchical CKM matrix with image, image, image, where image, in excellent agreement with observation.