Discrete Symmetry and GUT Breaking

We study the supersymmetric GUT models where the supersymmetry and GUT gauge symmetry can be broken by the discrete symmetry. First, with the ansatz that there exist discrete symmetries in the branes’ neighborhoods, we discuss the general reflection Z2 symmetries and GUT breaking on M 4 × M1 and M4 × M1 × M1. In those models, the extra dimensions can be large and the KK states can be set arbitrarily heavy. Second, considering the extra space manifold is the annulus A2 or disc D2, we can define any Zn symmetry and break any 6-dimensional N = 2 supersymmetric SU(M) models down to the 4-dimensional N = 1 supersymmetric SU(3) × SU(2) × U(1)M−4 models for the zero modes. In particular, there might exist the interesting scenario on M4 × A2 where just a few KK states are light, while the others are relatively heavy. Third, we discuss the complete global discrete symmetries on M4 × T 2 and study the GUT breaking. PACS: 11.10.Kk; 11.25.Mj; 04.65.+e; 11.30.Pb