Local Supersymmetry (N = 1)

Abstract

In this chapter we will study the implications of the hypothesis that the parameters of supersymmetry transformation ε become a function of space-time, i.e., ε = ε(x). We know, from Chapter 1, that invariance under local symmetry requires new fields in the theory which have spin 1, and have the same number of components as the number of independent parameters in the group. In analogy, local supersymmetry will require the introduction of the spin 3/2 field which is the Majorana type. This will bring us into a completely new domain of particle physics where new spin 3/2 elementary fields interact with ordinary matter fields. Furthermore, there will also be analogs of the Higgs mechanism once supersymmetry is spontaneously broken (the so-called super-Higgs effect). There is, however, a much more profound aspect to local supersymmetry. Once the spin 3/2 fields are introduced, to make the theory supersymmetric in the high spin sector, it will turn out that we will require a massless spin 2 field which can be identified with the graviton field g _μυ , thus “unifying” gravitation with the other three forces of nature. This discovery was made independently by Freedman, Ferrara, and Van Niuen-huizen [1], and by Deser and Zumino [1], and opened up a whole new possibility, not only of unification of gravity with particle physics [2] but also of new consequences for particle physics with supersymmetry. We will call the spin 3/2 particle gravitino and denote it by a Majorana field Ψ _μ .