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.

arXiv comment41 pages, 1 figure

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• Yukawa couplings in 6D gauge-Higgs unification on $T^2/Z_N$ with magnetic fluxes
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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
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• Brane-localized masses in magnetic compactifications
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• Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
• Superfield description of (4+2n)-dimensional SYM theories and their mixtures on magnetized tori
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Supersymmetric models on magnetized orbifolds with flux-induced Fayet-Iliopoulos terms
• Active Dirac Neutrinos via $SU(2{)}_L$ Doublets in 5d
• 4D effective action from non-Abelian DBI action with magnetic flux background
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• 5d Dirac fermion on quantum graph
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• Yukawa textures in modular symmetric vacuum of magnetized orbifold models