Classification of three generation models by orbifolding magnetized $T^2 \times T^2$

TL;DR

This paper classifies three-generation models derived from magnetized toroidal orbifolds with permutation and twist symmetries, analyzing their Yukawa couplings and modular symmetries, and explores their implications for quark masses and mixing.

Contribution

It introduces a systematic classification of three-generation models on magnetized $T^2 imes T^2$ orbifolds with permutation and twist orbifoldings, including analysis of Yukawa couplings and modular symmetry.

Findings

Classified possible three-generation models with non-zero Yukawa couplings.

Analyzed the modular symmetry properties of these orbifold models.

Demonstrated a model realizing realistic quark masses and mixing angles.

Abstract

We study orbifolding by the $\mathbb{Z}_2^{\rm (per)}$ permutaion of $T^2_1 \times T^2_2$ with magnetic fluxes and its twisted orbifolds. We classify the possible three generation models which lead to non-vanishing Yukawa couplings on the magnetized $T^2_1 \times T^2_2$ and orbifolds including the $\mathbb{Z}_2^{\rm (per)}$ permutation and $\mathbb{Z}_2^{\rm (t)}$ twist. We also study the modular symmetry on such orbifold models. As an illustrating model, we examine the realization of quark masses and mixing angles.