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

Flavor physics without flavor symmetries

“…The couplings between bulk Higgs and matter fields are calculated as overlap integrals of wave functions that have nontrivial profiles in the magnetized extra dimensions [31]. In a similar way, Yukawa couplings of magnetized toroidal orbifolds have been analyzed [32][33][34][35][36][37]. The resulting flavor structure depends on the number of pairs of Higgs doublets.…”

Wavefunctions on S2 with flux and branes

“…In particular, for fixed φ k , overlap integrals can become much more hierarchical because of strong localizations of wavefunctions, and then an overlap integral of the mode functions localized around the north pole and around the south pole becomes much smaller due to the branes. 7) 7) We can check that the bosonic wavefunction |φ k | is also localized at some point due to branes. Figure 3: Profiles of absolute values of spinor wavefunctions on the S 2 with two branes in terms of the modified l-coordinate.…”

Majorana neutrino mass structure induced by rigid instantons on toroidal orbifold

“…7 Moreover, it is found that non-Abelian discrete flavor symmetries appear at perturbative level in heterotic orbifold models [17,31] and intersecting/magnetized brane models [32,33]. 8 For three-generation models on magnetized orbifold models, see, e.g., [26,34], and those would correspond to T-duals of intersecting D-brane models. 9 More precisely, there is one more parameter, the overall scales of Higgs VEVs.…”