Theory of flavors: String compactification

Abstract

We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through $Z_{12-I}$ orbifold compactification. It is beyond presenting just three families of the standard model but is the first example from string compactification successfully fitting to the observed data. Assuming that all Yukawa couplings from string compactification are real, we also comment on a relation between the CP phases in the Jarlskog determinants obtained from the CKM and PMNS matrices. The flipped SU(5) model leads to the doublet-triplet splitting and possible proton decay operators. It is shown that the vacuum expectation values can be tuned such that the proton lifetime is long enough.