Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds

Abstract

We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of ${\mathrm{\ensuremath{\Gamma}}}_{N}$ for $N=3$, 4, 5, 7, 8, 16, that is, covering groups of $\mathrm{\ensuremath{\Delta}}(6(N/2{)}^{2})$ for $N=\mathrm{even}$ and central extensions of $PSL(2,{\mathbb{Z}}_{N})$ for $N=\mathrm{odd}$ with Scherk-Schwarz phases. We also study anomaly behaviors.