Abstract: |
In the modular invariant flavor model, the quark and lepton mass matrices are given in terms of modular forms which are holomorphic functions of a complex parameter, the modulus \tau. Residual symmetries arise whenever the VEV of the modulus \tau break the modular group only partially. Fixed points of modulus are the case. There are only two inequivalent finite points in the fundamental domain of \tau, \tau = i and \omega. Nearby those fixed points, fermion mass hierarchy and spontaneous CP violation can be realized. In this seminar, we briefly review the modular invariant flavor model. And then, we present typical modular A4 invariant models of quarks and leptons to reproduce fermion mass hierarchy and spontaneous CP violation. |