Introduction to supersymmetry

Abstract

The basic features of supersymmetric field theories are presented in this article, emphasizing the structure of the representations of the supersymmetry algebra. In Chapter 1, the simple and N-extended supersymmetry algebras are presented, and the representations on massive and massless states derived using Wigner's method of induced representations. In Chapter 2, the representations of the supersymmetry algebra on fields are introduced, together with the superspace formalism, which is applied to a discussion of the basic supersymmetric model, the Wess-Zumino model. In Chapter 3, supersymmetric Yang-Mills theories are discussed, and the formalism of superspace applied to the quantization of the Wess-Zumino model and supersymmetric Yang-Mills theories, and also to the analysis of the quantum supercurrent for conformally invariant and non-conformally-invariant theories. In Chapter 4, the technique of superspace quantization is applied to the maximal supersymmetic gauge theory, the N=4 supersymmetric Yang-Mills theory. This theory is finite to all orders in perturbation theory, as can be shown using manifestly N=2 supersymmetric Feynman rules.