Consistency of anomalies in susy gauge theories

We consider two problems in supersymmetric gauge theories - the anomaly supermultiplet and the calculation of the exact β functions in perturbation theory - which turn out to be interrelated. The main findings are:(i) generalization of the non-renormalization theorems for gauge F terms ∫ d²θ W²;(ii) solution of the anomaly puzzle and superextension of the Adler-Bardeen theorem;(iii) a constructive algorithm for computation of all-order terms in β functions;(iv) a new bosonic anomaly counting the number of the bosonic zero modes. We also show that Z factors of the matter superfields affect the magnitude of the observable gauge coupling. The basic technical element which ensured the breakthrough is the use of the Wilson operator expansion and distinction between the Wilson effective action Sw and the generator of 1PI vertices γ.