Lepton sector in modular A4 and gauged U(1)R symmetry

We propose a lepton model under modular A4 and gauged U(1)R symmetries in a supersymmetric framework, in which the neutrino masses are induced at one-loop level. Thanks to the modular A4 symmetry, we have several predictions on the lepton sector, especially, on fixed points of the vacuum expectation value of the modulus τ=i,ω(≡e2πi/3),i∞ each of which has remnant symmetry; Z2 for τ=i and Z3 for τ=ω,i∞. These points are favored by a string theory and are phenomenologically interesting. We examine favored parameter spaces in the models and also show that the lepton flavor violation in the models is smaller enough than the current experimental constraints.