Low Energy 6-Dimensional N=2 Supersymmertric SU(6) Models on $T^2$ Orbifolds

Abstract

We propose low energy 6-dimensional N=2 supersymmetric SU(6) models on $M^4\times T^2/(Z_2{)}^3$ and $M^4\times T^2/(Z_2{)}^4$, where the orbifold $SU(3{)}_C\times SU(3)$ model can be embedded on the boundary 4-brane. For the zero modes, the 6-dimensional N=2 supersymmetry and the SU(6) gauge symmetry are broken down to the 4-dimensional N=1 supersymmetry and the $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y\times U(1{)}^{\prime }$ gauge symmetry by orbifold projections. In order to cancel the anomalies involving at least one $U(1{)}^{\prime }$, we add extra exotic particles. We also study the anomaly free conditions and present some anomaly free models. The gauge coupling unification can be achieved at $100\sim 200$ TeV if the compactification scale for the fifth dimension is $3\sim 4$ TeV. The proton decay problem can be avoided by putting the quarks and leptons/neutrinos on different 3-branes. And we discuss how to break the $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y\times U(1{)}^{\prime }$ gauge symmetry, solve the $\mu$ problem, and generate the $Z-Z^{\prime }$ mass hierarchy naturally by using the geometry. The masses of exotic particles can be at the order of 1 TeV after the gauge symmetry breaking. We also forbid the dimension-5 operators for the neutrino masses by $U(1{)}^{\prime }$ gauge symmetry, and the realistic left-handed neutrino masses can be obtained via non-renormalizable terms.

arXiv commentLatex, 33 pages, discussion and references added

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• Gauge-Fermion Unification and Flavour Symmetry
• Gauge and Yukawa couplings in 6D supersymmetric SU(6) models
• Top SU(5) Models: Baryon and Lepton Number Violating Resonances at the LHC