$Z_N$ twisted orbifold models with magnetic flux

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.

34 pages, 4 figures

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• Modular forms of finite modular subgroups from magnetized D-brane models
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• Classification of three-generation models on magnetized orbifolds
• Zero-modes on orbifolds : magnetized orbifold models by modular transformation
• Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
• Gaussian Froggatt-Nielsen mechanism on magnetized 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
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• Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli stabilization
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• Non-invertible flavor symmetries in magnetized extra dimensions
• Inflation from periodic extra dimensions
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• Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux
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• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Wilson lines and UV sensitivity in magnetic compactifications
• Realistic three-generation models from SO(32) heterotic string theory
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• Realization of lepton masses and mixing angles from point interactions in an extra dimension
• Zero-mode counting formula and zeros in orbifold compactifications
• Texture zeros of quark mass matrices at fixed point $\tau =\omega$ in modular flavor symmetry
• Majorana neutrino mass structure induced by rigid instatons on toroidal orbifold
• Brane-localized masses in magnetic compactifications
• Index theorem on magnetized blow-up manifold of $T^2/{\mathbb{Z}}_N$
• Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models
• Wavefunctions and Yukawa Couplings on Resolutions of $T^2/{\mathbb{Z}}_N$ Orbifolds
• Index theorem on $T^2/{\mathbb{Z}}_N$ orbifolds
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• Remark on modular weights in low-energy effective field theory from type II string theory
• 6D gauge-Higgs unification on T^2/Z_N with custodial symmetry
• Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
• Magnetized orbifolds and localized flux
• Index and winding numbers on $T^2/{\mathbb{Z}}_N$ orbifolds with magnetic flux
• Kähler moduli stabilization in semi-realistic magnetized orbifold models
• Modular symmetry and zeros in magnetic compactifications
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Supersymmetric models on magnetized orbifolds with flux-induced Fayet-Iliopoulos terms
• Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua
• Zero-modes in magnetized $T^6/{\mathbb{Z}}_N$ orbifold models through $Sp(6,\mathbb{Z})$ modular symmetry
• Flavor structure of magnetized $T^2/{\mathbb{Z}}_2$ blow-up models
• Active Dirac Neutrinos via $SU(2{)}_L$ Doublets in 5d
• 5d Dirac fermion on quantum graph
• Seesaw mechanism in magnetic compactifications
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• Family number, Wilson line phases and hidden supersymmetry
• Quark mass matrices in magnetized orbifold models with localized Fayet-Iliopoulos terms
• Majorana neutrino masses by D-brane instanton effects in magnetized orbifold models
• Zero-mode product expansions and higher order couplings in gauge backgrounds
• Three-generation solutions of equations of motion in heterotic supergravity
• One-loop vacuum energy in 10D super-Yang-Mills theory on magnetized tori with/without 4D N=1 supersymmetric completion
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models