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Modular $A_4$ symmetric inverse seesaw model with $SU(2)_L$ multiplet fields

We propose an inverse seesaw model with large $SU(2)_L$ multiplets applying modular $A_4$ symmetry where $SU(2)_L$ quartet and septet fermions are introduced as triplets under the symmetry. The neutral components of the quartet contribute to mass matrix for inverse seesaw mechanism and interactions involving the septet induce Majorana mass terms of these extra fermions. Although there are several free parameters in the mass matrix we can obtain some predictions for observables in neutrino sector such as CP phases, sum of neutrino mass and effective mass for neutrinoless double beta decay, especially around fixed points of modulus motivated by string theories.