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 T₁² T₂² 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 Tᵢ² T i 2. Such a constraint can be derived from the moduli stabilization. The modular symmetry of T₁² T₂² T 1 2 × T 2 2 is SL (2, Z) 䃑 SL (2, Z) 䃒 Sp (4, Z) 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.