Magnetized orbifold models

We study (4+2n)-dimensional N=1 super Yang-Mills theory on the orbifold background with non-vanishing magnetic flux. In particular, we study zero-modes of spinor fields. The flavor structure of our models is different from one in magnetized torus models, and would be interesting in realistic model building.Comment: 26 page

Non-Abelian Discrete Symmetries in Particle Physics

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for $S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$, $\Sigma(3N^3)$ and $\Delta(6N^2)$, which have been applied for model building in the particle physics. We also present typical flavor models by using $A_4$, $S_4$, and $\Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.Comment: 179 pages, 8 figures, section 15 is changed, some references are adde

Flavor structure from magnetic fluxes and non-Abelian Wilson lines

We study the flavor structure of 4D effective theories, which are derived from extra dimensional theories with magnetic fluxes and non-Abelian Wilson lines. We study zero-mode wavefunctions and compute Yukawa couplings as well as four-point couplings. In our models, we also discuss non-Abelian discrete flavor symmetries such as $D_4$, $\Delta(27)$ and $\Delta(54)$.Comment: 27 page

CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration

We study physical implications of general CP symmetry including CP-like symmetry. Various scattering amplitudes of CP asymmetry are calculated in CP-like symmetric models. We explicitly show that the CP-like transformation leads to a specific relation between different CP asymmetries. The resultant relation is similar to the one obtained in GUT baryogenesis and sphaleron processes, where we also obtain a required condition for generating particle number asymmetry in CP-like symmetric models. In addition, we propose a generalization of a CP-like transformation for continuous symmetry groups. Since the CP transformation is an outer automorphism, which depends on the internal symmetry group, it turns out that the physical CP and CP-like symmetries can be mutually converted through the spontaneous symmetry breaking (SSB) of the internal symmetry. We investigate properties of physical CP asymmetry in both CP and CP-like symmetric phases, and find that the spontaneous CP violation and restoration can be observed even in models with continuous groups. We demonstrate that CP-like symmetric models with continuous Lie groups can be naturally realized in physical CP symmetric models through the SSB.Comment: 50 pages, 1 figur