Perturbation theory and renormalization of supersymmetric Yang-Mills theories

Abstract

We solve the problem of introducing, in supersymmetric Yang-Mills Lagrangians, a supersymmetric gauge breaking term and a Faddeev-Popov ghost interaction term. The resulting Lagrangian turns out to be invariant under a global symmetry transformation which is the supersymmetric extension of the Slavnov symmetry. We show that the complete analysis of all primitively divergent supergraphs ensures, in conjunction with the Slavnov identities, the renormalizability of the theory, once a supersymmetric and gauge invariant regularizing procedure has been introduced. We find that the simplest regularizing procedure is a generalization of the higher covariant derivatives method. In the case of interaction with matter fields we prove that no mass counter term is needed, in exact analogy with the model without gauge fields. Finally we show that, in the Abelian situation, a supersymmetric mass term for the vector multiplet can be introduced without spoiling the renormalizability, thus providing the supersymmetric extension of massive vector bosons theories.