Flavor symmetries from modular subgroups in magnetized compactifications

Abstract

Abstract We study the flavor structures of zero-modes, which are originated from the modular symmetry on T 1 2 × T 2 2 $$ {T}_1^2\times {T}_2^2 $$ 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 $$ {T}_1^2\times {T}_2^2 $$ is SL 2 ℤ τ 1 × SL 2 ℤ τ 2 ⊂ Sp 4 ℤ $$ \textrm{SL}{\left(2,\mathbb{Z}\right)}_{\tau_1}\times \textrm{SL}{\left(2,\mathbb{Z}\right)}_{\tau_2}\subset \textrm{Sp}\left(4,\mathbb{Z}\right) $$ 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.

Keywords

• Discrete Symmetries
• Flavour Symmetries