Non-Abelian Discrete Flavor Symmetries on Orbifolds

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.