Classifications of magnetized T4 and T4/Z2 orbifold models

We study constructions and classifications of three-generation models based on magnetized T4 and T4/Z2 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. We classify three-generation models 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.