Gauge Symmmetry and Supersymmetry Breaking by Discrete Symmetry

We study the principles of the gauge symmetry and supersymmetry breaking due to the local or global discrete symmetries on the extra space manifold. We show that the gauge symmetry breaking by Wilson line is the special case of the discrete symmetry approach where all the discrete symmetries are global and act freely on the extra space manifold. As applications, we discuss the N = 2 supersymmetric SO(10) and E8 breaking on the space-time M 4×A2 and M4×D2, and point out that similarly one can study any N = 2 supersymmetric SO(M) breaking. We also comment on the one-loop effective potential, the possible questions and generalization. PACS: 11.25.Mj; 11.10.Kk; 04.65.+e; 11.30.Pb