Abstract: |
It is known that the superstring theory on certain compactifications can lead to non-Abelian symmetries. Indeed, the torus compactification gives the modular symmetry. The modular group includes S3, A4, S4, and A5 as its subgroups. They are supposed to be symmetries in the flavor space. Coupling constants such as Yukawa couplings also transform non-trivially under the modular symmetry and are written as functions of the modulus called modular forms. The flavor structure of the mass matrices are essentially given by fixing the expectation value of the modulus, which is the only source of the breaking of the modular invariance. In this aspect, an attractive Ansatz was proposed by Feruglio, where A4 symmetry was taken. Along with this work, S3 and S4 symmetries have been discussed in the neutrino mixing. These approaches would make a bridge between flavor physics and underlying theory from the viewpoint of flavor symmetries. In my talk, we present a brief review in this field, and then discuss the modular invariant neutrino mass matrix. |