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.
Highlights
Torus compactifications with some magnetic fluxes are quite interesting extradimensional backgrounds [1,2,3,4,5].1 That can realize chiral spectra in four-dimensional low energy effective field theory
We propose new backgrounds of extra dimensions to lead to four-dimensional chiral models with three generations of matter fermions, that is T 2/ZN twisted orbifolds with magnetic fluxes
We have studied the U(1) gauge theory on the T 2/ZN orbifolds with magnetic fluxes, Scherk-Schwarz phases and Wilson line phases
Summary
We review the U(1) gauge theory on a two-dimensional torus with magnetic flux following ref. [5, 54]. It should be emphasized that all of the Wilson line phase and the Scherk-Schwarz phases can be arbitrary, but are not physically independent because the Wilson line phase can be absorbed into the Scherk-Schwarz phases by a redefinition of fields and vice versa (see appendix B). This fact implies that we can take, for instance, the basis of vanishing Wilson line phases, without any loss of generality. It is interesting to point out that allowed Scherk-Schwarz phases are severely restricted for T 2/ZN orbifold models, as we will see while there is no restriction on the Scherk-Schwarz phases for T 2 models
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