Applications of exact renormalization group techniques to the non-perturbative study of supersymmetric gauge field theory

Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of suc h theories. Starting from the ultra-violet finite mass deformed N = 4 super symmetric Yang-Mills theory, one varies the regularising mass and compensat es for it by introducing an effective Wilsonian action. (Polchinski's) reno rmalization group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-fu nction. When supersymmetry is broken up to N = 1 the form of effective acti ons in terms of massless fields is quite reasonable, while in the case of t he N = 2 model we appear to have problems related to instantons.