Flavor symmetries from modular subgroups in magnetized compactifications

TL;DR

This paper explores how modular symmetries in magnetized compactifications on tori influence flavor structures, deriving specific flavor groups through moduli constraints and symmetry breaking.

Contribution

It introduces a moduli constraint that breaks the modular symmetry to specific subgroups, leading to new flavor group structures in magnetized compactification models.

Findings

Moduli constraint $ au_2=N au_1$ derived from stabilization.

Modular symmetry breaks to $\Gamma_0(N) imes \Gamma^0(N)$.

Wave functions correspond to covering groups of these symmetries.

Abstract

We study the flavor structures of zero-modes, which are originated from the modular symmetry on $T^2_1\times T^2_2$ and its orbifold with magnetic fluxes. We introduce the constraint on the moduli parameters by $\tau_2=N\tau_1$, where $\tau_i$ denotes the complex structure moduli on $T^2_i$. Such a constraint can be derived from the moduli stabilization. The modular symmetry of $T^2_1 \times T^2_2$ is $SL(2,\mathbb{Z})_{\tau_1} \times SL(2,\mathbb{Z})_{\tau_2} \subset Sp(4,\mathbb{Z})$ and it is broken to $\Gamma_0(N) \times \Gamma^0(N)$ by the moduli constraint. The wave functions represent their covering groups. We obtain various flavor groups in these models.