Abstract:We propose new backgrounds of extra dimensions to lead to four-dimensional chiral models with three generations of matter fermions, that is T 2 /Z N twisted orbifolds with magnetic fluxes. We consider gauge theory on six-dimensional space-time, which contains the T 2 /Z N orbifold with magnetic flux, Scherk-Schwarz phases and Wilson line phases. We classify all the possible Scherk-Schwarz and Wilson line phases on T 2 /Z N orbifolds with magnetic fluxes. The behavior of zero modes is studied. We derive the number of zero modes for each eigenvalue of the Z N twist, showing explicitly examples of wave functions. We also investigate Kaluza-Klein mode functions and mass spectra.

We propose a new model which can simultaneously and naturally explain the origins of fermion generation, quark mass hierarchy, and the Cabibbo-Kobayashi-Maskawa matrix from the geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermions at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of the nondiagonal elements of fermion mass matrices is found to be severely restricted due to the geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy. a Recently, the ATLAS and CMS experimental groups of the CERN Large Hadron Collider (LHC) have announced the excess at 125 GeV, which is consistent with the Standard Model (SM) Higgs boson, with a local significance of 5σ after combining 7 TeV and 8 TeV data [1,2]. This amazing happening means that the mysteries behind the last missing piece of the SM are ready to be unveiled. But the SM still has many points which are unclear, in spite of lots of effort from physicists.One is called the "quark mass hierarchy problem". In the SM, we are forced to comply with a hierarchy of almost five orders of magnitude in Yukawa couplings of quarks for describing the suitable quark masses. Closely related to this issue, the SM cannot answer the mechanism behind the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which describes the strengths of generationchanging interactions in the SM. In addition to these two issues, we cannot explain why we introduce three copies of quarks whose quantum numbers are the same except for their masses and the degrees of mixings in the above interactions. Many attempts have been made to explain the issues within the four-dimensional (4D) Quantum Field Theory (QFT) framework with, including, for example, launching new continuous and/or discrete symmetries, introducing new matter and interactions, and discussing renormalization group (RG) effects from a theory at a (very) high energy scale compared to the electroweak (EW) scale.When we focus on the case in five dimensions (5D), where there is one additional spatial direction, we can find a new useful tool for tackling the above and other problems: geometry. Two of the most renowned studies which show the power of geometry are [3,4], where the authors proposed innovative ways for solving the hierarchy problem. Extra space can have a huge variety of structure, which are detected as differences from the 4D effective theory point of view. In a 5D QFT framework, we also find new mechanisms which we cannot find in 4D, for example, generating spontaneous gauge symmetry breaking with a global Wilson loop operator [5][6][7], and symmetry br...

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

We propose a mechanism to obtain the generation of matter in the standard model. We start from the analysis of the $T^2/Z_N$ shifted orbifold with magnetic flux, which imposes a $Z_N$ symmetry on torus. We also consider several orbifolds such as $(T^2\times T^2)/Z_N$, $(T^2 \times T^2 \times T^2)/(Z_N \times Z_{N'})$ and $(T^2 \times T^2 \times T^2)/(Z_N \times Z_{N'} \times Z_{N"})$. On such orbifolds, we study the behavior of fermions in two different means, one is the operator formalism and the other is to analyze wave functions explicitly. For an interesting result, it is found that the number of zero-mode fermions is related to $N$ of the $Z_N$ symmetry. In other words, the generation of matter relates to the type of orbifolds. Moreover, we find that shifted orbifold models to realize three generations are, in general, severely restricted. For example, the three-generation model on the type of $M^4 \times (T^2 \times T^2)/Z_N$ is unique. One can also construct other types of three-generation orbifold models with rich flavor structure. Those results may bring us a realistic model with desired Yukawa structure.Comment: 32 pages, 1 figur

We investigate a model on an extra dimension S 1 where plenty of effective boundary points described by point interactions (zero-thickness branes) are arranged. After suitably selecting the conditions on these points for each type of five-dimensional fields, we realize the tiny active neutrino masses, the charged lepton mass hierarchy, and lepton mixings with a CP-violating phase, simultaneously. Not only the quark's but also the lepton's configurations are generated in a unified way with acceptable accuracy, with neither the see-saw mechanism nor symmetries in Yukawa couplings, by suitably setting the model parameters, even though their flavor structures are dissimilar each other. One remarkable point is that a complex vacuum expectation value of the five-dimensional Higgs doublet in this model becomes the common origin of the CP violation in both quark and lepton sectors. The model can be consistent with the results of the precision electroweak measurements and Large Hadron Collider experiments.