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We study (4+2n)-dimensional N=1 super Yang-Mills theory on the orbifold background with non-vanishing magnetic flux. In particular, we study zero-modes of spinor fields. The flavor structure of our models is different from one in magnetized torus models, and would be interesting in realistic model building.
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We study three generation models in the four-dimensional spacetime, which can be derived from the ten-dimensional N=1 super Yang-Mills theory on the orbifold background with a non-vanishing magnetic flux. We classify the flavor structures and show possible patterns of Yukawa matrices. Some examples of numerical studies are also shown.
We study Kahler moduli stabilizations in semi-realistic magnetized D-brane models based on $ Z_2times Z_2$ toroidal orbifolds. In type IIB compactifications, 3-form fluxes can stabilize the dilaton and complex structure moduli fields, but there remain some massless closed string moduli fields, Kahler moduli. The magnetic fluxes generate Fayet-Iliopoulos terms, which can fix ratios of Kahler moduli. On top of that, we consider D-brane instanton effects to stabilize them in concrete D-brane models and investigate the brane configurations to confirm that the moduli fields can be stabilized successfully. In this paper, we treat two types of D-brane models. One is based on D9-brane systems respecting the Pati-Salam model. The other is realized in a D7-brane system breaking the Pati-Salam gauge group. We find suitable configurations where the D-brane instantons can stabilize the moduli fields within both types of D-brane models, explaining an origin of a small constant term of the superpotential which is a key ingredient for successful moduli stabilizations.
We study magnetized orbifold models. We assume the localized Fayet-Iliopoulos terms and the corresponding gauge background. Such terms lead to strong localization of zero-mode wavefunc- tions. In this setup, we compute quark mass matrices.
We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called $mu$-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. The zero-mode degeneracy to be identified as the generation in four-dimensional (4D) effective theories is determined by the magnetic fluxes. It is known that multiple Higgs zero-modes appear in general in magnetized orbifold models. We derive the analytic form of the $mu$-term matrix in the 4D effective theory generated by the localized sources on $T^2/Z_2$ orbifold fixed points, and find that this matrix can lead to a distinctive pattern of the eigenvalues that yields hierarchical $mu$-terms for the multiple Higgs fields. The lightest ones can be exponentially suppressed due to the localized wavefunctions of zero-modes determined by the fluxes, while the others are of the order of the compactification scale, which can provide a dynamical origin of the electroweak scale as well as a simultaneous decoupling of extra Higgs fields. We also show that a certain linear combination of the lightest Higgs fields could generate the observed mass ratios of down-type quarks through their Yukawa couplings determined by the wavefunctions.
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.
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