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 such theories. Starting from the ultra-violet finite mass deformed N = 4 supersymmetric Yang-Mills theory, one varies the regularising mass and compensates for it by introducing an effective Wilsonian action. (Polchinski's) renormalization group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-function. When supersymmetry is broken up to N = 1 the form of effective actions in terms of massless fields is quite reasonable, while in the case of the N = 2 model we appear to have problems related to instantons.