Exact $\beta$-function in Abelian and non-Abelian $\mathcal{N}=1$ supersymmetric gauge models and its analogy with QCD $\beta$-function in C-scheme

Abstract

For $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the renormalization group $\beta$-function, defined in terms of the renormalized coupling constant, is valid. These schemes are related with each other by finite renormalizations forming a one-parameter commutative subgroup of general renormalization group transformations. The analogy between the exact $\beta$-function in $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter and the $\beta$-function of quantum chromodynamics in the C-scheme is discussed.