Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models

TL;DR

This paper systematically classifies three-generation models on magnetized $T^4$ and $T^4/Z_2$ orbifolds, analyzing chiral zero modes, gauge field freedoms, and Higgs sector configurations to understand their relationships and diversity.

Contribution

It provides a comprehensive classification of models with magnetic fluxes and Scherk-Schwarz phases on orbifolds, revealing the structure and variety of possible three-generation configurations.

Findings

Infinite three-generation models identified

Systematic classification clarifies relationships between models

Higgs sector configurations analyzed in detail

Abstract

We study constructions and classifications of three-generation models based on magnetized $T^4$ and $T^4/{Z}_2$ orbifold as candidates of the compact space. We focus on chiral fermion zero-mode wave functions in the extra dimensions. Freedoms of constant gauge fields, called Scherk-Schwarz phases are taken into account. Infinite number of three-generation models are yielded, corresponding to the ways in which the magnetic flux can be turned on. We classify them in a systematic manner, clarifying the relationship between different models. The Higgs sector is also studied by analyzing possible assignments of the magnetic flux and Scherk-Schwarz phases, etc. to left- and right-handed fermions.