NSVZ Relation and NSVZ Scheme in $$\mathcal{N} = 1$$ Non-Abelian Supersymmetric Gauge Theories

Abstract

We briefly describe the perturbative derivation of the exact NSVZ $$\beta $$ -function for $$\mathcal{N} = 1$$ supersymmetric non-Abelian gauge theories in the case of using the higher covariant derivative regularization. It is demonstrated that with this regularization the NSVZ equation written in the form of a relation between the $$\beta $$ -function and the anomalous dimensions of the quantum superfields is satisfied by the renormalization group functions defined in terms of the bare couplings independently of a renormalization prescription. For the renormalization group functions defined in terms of the renormalized couplings this implies that one of the NSVZ schemes in all loops is given by the HD+MSL prescription, when the theory is regularized by higher derivatives and the renormalization constants contain only powers of $$ln\Lambda {\text{/}}\mu $$ . All these statements are verified by comparing certain terms in the three-loop $$\beta $$ -function with the corresponding contributions to anomalous dimensions of the quantum superfields.