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The perturbative $\beta$-function is known exactly in a number ofsupersymmetric theories and in the 't Hooft renormalization scheme in the$\phi_4^4$ model. It is shown how this allows one to compute the effectiveaction exactly for certain background field configurations and to relate bareand renormalized couplings. The relationship between the MS and SUSYsubtraction schemes in $N = 1$ super Yang-Mills theory is discussed

The renormalization group with exact β-functions