Exact β-Function in Abelian and non-Abelian $${\cal N} = 1$$ Supersymmetric Gauge Models and Its Analogy with the QCD β-Function in the C-scheme

Abstract

For $${\cal N} = 1$$ 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 β-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 β-function in $${\cal N} = 1$$ supersymmetric Yang-Mills theory without matter and the β-function of quantum chromodynamics in the C-scheme is discussed.