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

Predictive neutrino mass textures with origin of flavor symmetries

We investigate origins of predictive one-zero neutrino mass textures in a systematic way. Here we search Abelian continuous(discrete) global symmetries, and non-Abelian discrete symmetries, and show how to realize these neutrino masses. Then we propose a concrete model involving a dark matter candidate and an extra gauge boson, and show their phenomenologies.Comment: 23 pages, 3 figures, version accepted for publication in physical review

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

A Consolidation Problem and its Solution

As we know in civil engineering, it is the first task for constructing banks or building structures to predict the subsidence of the underlying ground. When ground of clay saturated with pore water is compressed, the water flows out and the total volume decreases. Consequently, the ground subsides and the strength of the clay increases. We call this phenomena consolidation. For the simplicity of analysis, we usually assume that the thickness of the clay stratum will not vary during consolidation and neglect the effect by its decrease. Alternatively in this paper, we formulate a mathematical model of one dimensional consolidation problem, taking the decrease of the thickness of the clay stratum into consideration. And we show the existence and uniqueness of the exact solution of the problem under the assumption of small initial data

Flavor landscape of 10D SYM theory with magnetized extra dimensions

We study the flavor landscape of particle physics models based on a ten-dimensional super Yang-Mills theory compactified on magnetized tori preserving four-dimensional ${\cal N}=1$ supersymmetry. Recently, we constructed a semi-realistic model which contains the minimal supersymmetric standard model (MSSM) using an Ansatz of magnetic fluxes and orbifolding projections. However, we can consider more various configurations of magnetic fluxes and orbifolding projections preserving four-dimensional ${\cal N}=1$ supersymmetry. We research systematically such possibilities for leading to MSSM-like models and study their phenomenological aspects.Comment: 24 pages, 3 figures. arXiv admin note: text overlap with arXiv:1211.431

More on the Isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4)

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3