Low energy six-dimensional N = 2 supersymmetric SU(6) models on T2 orbifolds

We propose low energy six-dimensional N = 2 supersymmetric SU(6) models on M4 x T2/(Z2)3 and M4 x T2/(Z2)4, where the orbifold SU(3)C x SU(3) model can be embedded on the boundary 4-brane. For the zero modes, the six-dimensional N = 2 supersymmetry and the SU(6) gauge symmetry are broken down to the four-dimensional N = 1 supersymmetry and the SU(3)C x SU(2)L x U(1)Y x U(1)' gauge symmetry by orbifold projections. In order to cancel the anomalies involving at least one U(1)', 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 100-200 TeV if the compactification scale for the fifth dimension is 3-4 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 x SU(2)L x U(1)Y x U(1)' gauge symmetry, solve the μ problem, and generate the Z - Z' 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-five operators for the neutrino masses by U(1)' gauge symmetry, and the realistic left-handed neutrino masses can be obtained via non-renormalizable terms