Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds

We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of ΓN for N = 3, 4, 5, 7, 8, 16, that is, covering groups of Δ (6 (N / 2)2) for N = even and central extensions of PSL (2, ZN) for N = odd with Scherk-Schwarz phases. We also study anomaly behaviors.