A linear seesaw model with $A_4$-modular flavor and local $U(1)_{B-L}$ symmetries

We discuss a linear seesaw model with local $U(1)_{B-L}$ and modular $A_4$ symmetries. The neutrino mass matrix for linear seesaw mechanism is realized by $U(1)_{B-L}$ charge assignment and the nature of modular $A_4$ symmetry. We formulate neutrino mass and carry our numerical analysis showing some predictions for observables in neutrino sector. Remarkably, the case of inverted neutrino mass ordering (IO) is realized by a specific region around $\tau=\omega=e^{2\pi i/3}$, which is favored by a string theory. Thus, our prediction would be very strong in case of IO.