Modular symmetry and non-Abelian discrete flavor symmetries in string compactification

TL;DR

This paper explores how modular symmetry in string compactifications relates to non-Abelian discrete flavor symmetries, specifically D4, in magnetized D-brane and heterotic orbifold models, revealing subgroup structures.

Contribution

It demonstrates that D4 flavor symmetry arises as a subgroup of the modular symmetry in specific string compactification models.

Findings

D4 flavor symmetry is a subgroup of the modular symmetry in magnetized D-brane models.

The same modular symmetry appears in heterotic orbifold models with $T^2/Z_4$.

Modular symmetry constrains flavor structures in string-derived models.

Abstract

We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The $T^2/Z_4$ orbifold model has the same modular symmetry as the magnetized brane model with $M=2$, and its flavor symmetry $D_4$ is a subgroup of the modular symmetry.