Z N twisted orbifold models with magnetic flux

Abstract

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.

6D gauge-Higgs unification on T 2 /Z N with custodial symmetry

“…This case is interesting because the hierarchical structure of the Yukawa coupling constants can be realized by the wave function localization [24,25], and the generation structure can also be obtained by a background magnetic flux [22]. In the following, we focus on the quark sector, but a similar argument is also applicable to the lepton sector.…”

“…In fact, when (N, n P , m ω ) = (3, 1, 0), the fermionic zero-modes from each 6D Dirac fermion contain 22) and when (N, n P , m ω ) = (3, 2, 2), they contain…”

“…The number of the zero-modes j max is determined by the magnetic flux [22]. The zero-mode functions f (j)µ χ 6 (z) are determined so that (5.3) satisfies the first two conditions in (5.2).…”

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

“…These degrees of freedom are equivalent to each other [28]. Hence, we restrict ourselves to Scherk-Schwarz phases.…”

“…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].…”