Classification of three-generation models on magnetized orbifolds

Abstract

We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on $T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously.

Comments: 28 pages (main body and references) + 65 pages (full list of classification), 22 tables (v1); typos corrected, problem in sentence fixed (v2)