Flavor symmetries from modular subgroups in magnetized compactifications

A bstract We study the flavor structures of zero-modes, which are originated from the modular symmetry on T 1 2 × T 2 2 and its orbifold with magnetic fluxes. We introduce the constraint on the moduli parameters by τ 2 = Nτ 1 , where τ i denotes the complex structure moduli on T i 2 . Such a constraint can be derived from the moduli stabilization. The modular symmetry of T 1 2 × T 2 2 is SL 2 ℤ τ 1 × SL 2 ℤ τ 2 ⊂ Sp 4 ℤ and it is broken to Γ 0 ( N ) × Γ 0 ( N ) by the moduli constraint. The wave functions represent their covering groups. We obtain various flavor groups in these models.