Right-handed Neutrinos in F-theory Compactifications

F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT scale, which is in nice agreement with the Delta m^2 of the atmospheric neutrino oscillation through the see-saw mechanism. We also discuss various scenarios of solving the dimension-4 proton decay problem in supersymmetric F-theory compactifications, along with considering the consequences of those scenarios in the nature of right-handed neutrinos.