N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E6 models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M4×S1/(Z2×Z2′)×S1/(Z2×Z2′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)2, SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)3 with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A2 and disc D2, we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)3 models for the zero modes, and give the simplest model with Z9 symmetry. We also comment on the extra gauge symmetry breaking and its generalization.