Shifted orbifold models with magnetic flux

Abstract

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 $(T^2\times T^2)/Z_N$, $(T^2\times T^2\times T^2)/(Z_N\times Z_{N^{\prime }})$ and $(T^2\times T^2\times T^2)/(Z_N\times Z_{N^{\prime }}\times Z_{N"})$. 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.

32 pages, 1 figure

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Cited by in corpus (28)

• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• $Z_N$ twisted orbifold models with magnetic flux
• Classification of three-generation models on magnetized orbifolds
• Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
• Operator analysis of physical states on magnetized $T^2/Z_N$ orbifolds
• Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes
• CP-violating phase on magnetized toroidal orbifolds
• $CP$ phase from twisted Higgs vacuum expectation value in extra dimension
• Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions
• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Wilson lines and UV sensitivity in magnetic compactifications
• Orbifold Family Unification on 6 Dimensions
• Flavor landscape of 10D SYM theory with magnetized extra dimensions
• Brane-localized masses in magnetic compactifications
• 4D modular flavor symmetric models inspired by higher dimensional theory
• 6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
• Superfield description of (4+2n)-dimensional SYM theories and their mixtures on magnetized tori
• Supersymmetry in 6d Dirac Action
• Orbifold family unification using vectorlike representation on six dimensions
• Active Dirac Neutrinos via $SU(2{)}_L$ Doublets in 5d
• The implication of gauge-Higgs unification to the hierarchical fermion masses
• 5d Dirac fermion on quantum graph
• Predictions of $SU(9)$ orbifold family unification
• Family number, Wilson line phases and hidden supersymmetry
• Effects of localized μ-terms at the fixed points in magnetized orbifold models
• Majorana neutrino masses by D-brane instanton effects in magnetized orbifold models
• One-loop vacuum energy in 10D super-Yang-Mills theory on magnetized tori with/without 4D N=1 supersymmetric completion