Operator analysis of physical states on magnetized T2/ZN 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. (Note: This article is registered under preprint number: arXiv:1409.5421.)

Zero-modes on orbifolds: Magnetized orbifold models by modular transformation

“…Similarly, we can obtain Z 4 eigenvalues and eigenstates by using explicit matrices, C j k;M for each value of M, in particular small values of M. Table II shows the numbers of Z 4 zero-modes for small values of M. This result is consistent with the previous results [28,29] up to the definition of the Z 4 twist. 4 The corresponding Z 4 eigenstates are shown in Appendix C.…”

“…Similarly, we can analyze the eigenvalues and eigenvectors for other M. Table IV shows the numbers of Z 3 zero-modes with each eigenvalue for small values of M. This result is consistent with the previous results [28,29]. We can derive eigenvectors, but their explicit forms are, in general, very complicated.…”

“…Zero-mode wave functions were studied by numerical studies [28] and the corresponding states were studied by operator analysis in quantum mechanism [29]. By use of those results, model building and fermion mass matrices were also studied [30][31][32].…”

Supersymmetric models on magnetized orbifolds with flux-induced Fayet-Iliopoulos terms

“…Next, we go on to the compactification on magnetized orbifolds. Systematic studies of Z N (N=3,4,6) orbifolds with magnetic fluxes have been recently done [10]. In this paper we concentrate on the Z 2 orbifolds [8,9], where all field contents are assigned into either even or odd modes under the Z 2 parity.…”

“…While the three-generation structure is uniquely given with a ∆ (27) flavor symmetry on magnetized tori without orbifolding, the orbifold projections as well as certain classes of Wilson-lines lead to a broad variety of three-generation structure with different types of flavor symmetries [7], and furthermore it can eliminate some phenomenologically disfavored extra massless field contents. The three-generation structures were systematically studied with Z 2 orbifolds [8,9] and Z 3,4,6 ones [10].…”