“…Moreover the addition of fermions in the higher-dimensional gauge theory leads naturally after CSDR to Yukawa couplings in four dimensions. In the successes of the CSDR scheme certainly should be added the possibility to obtain chiral theories in four dimensions [18,19,20,21] as well as softly broken supersymmetric or non-supersymmetric theories starting from a supersymmetric gauge theory defined in higher dimensions [22].…”
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields.
“…Moreover the addition of fermions in the higher-dimensional gauge theory leads naturally after CSDR to Yukawa couplings in four dimensions. In the successes of the CSDR scheme certainly should be added the possibility to obtain chiral theories in four dimensions [18,19,20,21] as well as softly broken supersymmetric or non-supersymmetric theories starting from a supersymmetric gauge theory defined in higher dimensions [22].…”
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields.
“…First, we show the prescriptions to identify gauge symmetry and field components which satisfy the constrants Eq (26), (27), (29). The gauge group H that satisfy the constraint Eq (26) is identified as…”
Section: A Gauge Symmetry and Particle Contents In Four-dimensionsmentioning
confidence: 99%
“…Gauge theories with the symmetry condition are well investigated to construct a model which provide Grand Unified Theory (GUT) in four-dimensions [22,26,27,28,29,30]. No known model, however, reproduced the full particle contents of GUTs.…”
We analyze a gauge-Higgs unification model which is based on a gauge theory defined on a six-dimensional spacetime with an S 2 extra-space. We impose a symmetry condition for a gauge field and non-trivial boundary conditions of the S 2 . We provide the scheme for constructing a four-dimensional theory from the six-dimensional gauge theory under these conditions. We then construct a concrete model based on an SO(12) gauge theory with fermions which lie in a 32 representation of SO (12), under the scheme. This model leads to a Standard-Model(-like) gauge theory which has gauge symmetry SU(3) × SU(2) L × U(1) Y (× U(1) 2 ) and one generation of SM fermions, in four-dimensions. The Higgs sector of the model is also analyzed, and it is shown that the electroweak symmetry breaking and the prediction of W-boson and Higgs-boson masses are obtained.
“…This advantage increases the chance for the higher-dimensional model to be a promising candidate. No theories have been found quite promising, however, for the 6, 10, and 14 dimensional spacetimes [22,26,29,30,31,32,33,34,35,36].…”
We investigate gauge-Higgs unification models in eight-dimensional spacetime
where extra-dimensional space has the structure of a four-dimensional compact
coset space. The combinations of the coset space and the gauge group in the
eight-dimensional spacetime of such models are listed. After the dimensional
reduction of the coset space, we identified $\mathrm{SO}(10)$, $\mathrm{SO}(10)
\times \mathrm{U}(1)$ and $\mathrm{SO}(10) \times \mathrm{U}(1) \times
\mathrm{U}(1)$ as the possible gauge groups in the four-dimensional theory that
can accomodate the Standard Model and thus is phenomenologically promising.
Representations for fermions and scalars for these gauge groups are tabulated.Comment: 7 page
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