Non-Abelian Discrete Flavor Symmetries on Orbifolds

TL;DR

This paper explores how non-Abelian discrete flavor symmetries like $D_N$, $ ext{S}_4$, and $A_4$ can be realized in extra-dimensional models on specific orbifolds, expanding the toolkit for flavor symmetry model building.

Contribution

It demonstrates the realization of various non-Abelian flavor symmetries and their subgroups on orbifolds $S^1/Z_2$ and $T^2/Z_3$, including $A_4$ and $S_4$, in extra-dimensional models.

Findings

Realization of $D_N$, $ ext{S}_4$, $A_4$ symmetries on orbifolds.

Construction of models with $S_3$ flavor symmetry on different orbifolds.

Identification of subgroups like $Q_N$, $T_7$ within the orbifold framework.

Abstract

We study non-Abelian flavor symmetries on orbifolds, $S^1/Z_2$ and $T^2/Z_3$. Our extra dimensional models realize $D_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$ and $\Delta(6N^2)$ including $A_4$ and $S_4$. In addition, one can also realize their subgroups such as $Q_N$, $T_7$, etc. The $S_3$ flavor symmetry can be realized on both $S^1/Z_2$ and $T^2/Z_3$ orbifolds.