Currents in supersymmetric theories

This chapter discusses the Ferrara-Zumino multiplet of currents. It is shown that the currents can belong to an alternative supermultiplet which can be used to derive a new formulation of N=1 supergravity. The connection between the multiplet of currents and the finiteness of the maximally extended super Yang-Mills theory is examined. Topics considered include currents in the Wess-Zumino model, the finiteness of N=4 Yang-Mills theory, the uniqueness of the multiplet of currents, and currents and auxiliary field. It is determined that although the superconformal currents, up to a technical assumption, belong to one unique multiplet, the multiplet of super-Poincare currents is not unique. The new formulation possesses a local U(1) chiral invariance and has different properties in its coupling to super-matter than the well known minimal formulation of supergravity