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

TL;DR

This paper explores the modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds, identifying specific finite groups and their representations, and analyzing anomaly behaviors.

Contribution

It introduces a classification of three-generation modes as representations of covering and extended groups of modular groups on magnetized orbifolds, including Scherk-Schwarz phases.

Findings

Identification of finite modular flavor groups for three-generation modes

Connection of modes to covering and extended groups of 94(6(N/2)^2) and PSL(2,)

Analysis of anomaly behaviors in these models

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 $\Gamma_N$ for $N=3,4,5,7,8,16$, that is, covering groups of $\Delta(6(N/2)^2)$ for $N=$ even and central extensions of $PSL(2,\mathbb{Z}_{N})$ for $N=$odd with Scherk-Schwarz phases. We also study anomaly behaviors.