Neutrino mass textures from F-theory

Experimental data on the neutrino mixing and masses strongly suggest an underlying approximate symmetry of the relevant Yukawa superpotential terms. Intensive phenomenological explorations during the last decade indicate that permutation symmetries such as S (4), A (4) and their subgroups, under certain assumptions and vacuum alignments, predict neutrino mass textures compatible with such data. Motivated by these findings, in the present work we analyze the neutrino properties in F-theory GUT models derived in the framework of the maximal underlying E (8) symmetry in the elliptic fibration. More specifically, we consider local F-SU(5) GUT models and study in detail spectral cover geometries with monodromies associated to the finite symmetries S (4),A (4) and their transitive subgroups, including the dihedral group D (4) and Z (2)xZ (2). We discuss various issues that emerge in the implementation of S (4),A (4) neutrino models in the F-theory context and suggest how these can be resolved. Realistic models are presented for the case of monodromies based on their transitive subgroups. We exemplify this procedure with a detailed analysis performed for the case of Z (2)xZ (2) model.