Discrete Symmetries in the MSSM

Abstract

The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z_4^R symmetry is discovered which solves the \mu-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z_4^R is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z_4^R symmetry and other desirable features.