Operator analysis of physical states on magnetized $T^2/Z_N$ orbifolds

Abstract

We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds $T^2/Z_3$, $T^2/Z_4$, $T^2/Z_6$ (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries.

41 pages, 1 figure

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• Massive modes in magnetized brane models
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Cited by in corpus (14)

• Classification of three-generation models on magnetized orbifolds
• Non-invertible flavor symmetries in magnetized extra dimensions
• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points
• Zero-mode counting formula and zeros in orbifold compactifications
• Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models
• Index theorem on $T^2/{\mathbb{Z}}_N$ orbifolds
• Index and winding numbers on $T^2/{\mathbb{Z}}_N$ orbifolds with magnetic flux
• Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Supersymmetric models on magnetized orbifolds with flux-induced Fayet-Iliopoulos terms
• 4D effective action from non-Abelian DBI action with magnetic flux background
• Majorana neutrino masses by D-brane instanton effects in magnetized orbifold models
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models