N= 2 Supersymmetric Yang-Mills Theories in the Wess-Zumino Gauge

Abstract

We have shown that one can study the renormalization of supersymmetric Yang-Mills theories in a way which does not depend on any particular renormalization scheme. Since there is no known reliable renormalization procedure which respects both BRS invariance and supersymmetry we have to assume that BRS and/or SUSY invariance are destroyed in the renormalized theory. This forces us and allows us to start from a more general Lagrangean having only those symmetries which are respected by the renormalization procedure (i.e. Lorentz invariance and a global SU(2) x SU(2)). The anomalies automatically satisfy Wess-Zumino consistency conditions which do or do not guarantee that the parameters in the effective action can be chosen in such a way that the renormalized theory is BRS and SUSY invariant (cohomology problem).

In spite of all the complications due to the non-linearities of the SUSY transformations in the Wess-Zumino gauge it is possible to analyze this cohomology problem (although this analysis is not yet entirely completed). At present we are able to show that the anomalies for BRS transformations and field dependent gauge transformations can be removed by suitable finite renormalizations. We are confident that the same can be done for the SUSY anomaly, i.e. that there is no genuine anomaly. Once this has been achieved, all parameters of the theory are determined by symmetry requirements and by a few (gauge invariant and supersymmetric) normalization conditions.