The Renormalization Group with Exact beta-Functions

Abstract

The perturbative $\beta$-function is known exactly in a number of supersymmetric theories and in the 't Hooft renormalization scheme in the ${\varphi }_4^4$ model. It is shown how this allows one to compute the effective action exactly for certain background field configurations and to relate bare and renormalized couplings. The relationship between the MS and SUSY subtraction schemes in $N=1$ super Yang-Mills theory is discussed.