Flavor symmetries from modular subgroups in magnetized compactifications - Tatsuo Kobayashi; Kaito Nasu; Ryusei Nishida; Hajime Otsuka; Shohei Takada (Journal of High Energy Physics)
Abstract We study the flavor structures of zero-modes, which are originated from the modular symmetry on T 1 2 × T 2 2 $$ T_1^2× T_2^2 $$ 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 $$ T_i^2 $$ . Such a constraint can be derived from the moduli stabilization. The modular symmetry of T 1 2 × T 2 2 $$ T_1^2× T_2^2 $$ is SL 2 ℤ τ 1 × SL 2 ℤ τ 2 ⊂ Sp 4 ℤ $$ SL{\left(2,\mathbb{Z}\right)}_{τ_1}× SL{\left(2,\mathbb{Z}\right)}_{τ_2}\subset Sp\left(4,\mathbb{Z}\right) $$ and it is broken to Γ0(N) × Γ0(N) by the moduli constraint. The wave functions represent their covering groups. We obtain various flavor groups in these models.