New form of the NSVZ relation at the two-loop level

Recently the exact NSVZ $\beta$-function was rewritten in the form of a relation between the $\beta$-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields. It was also suggested that this form of the NSVZ equation follows from an underlying equation relating two-point Green functions of the theory. Here we demonstrate that this relation is satisfied at the two-loop level for the non-Abelian $\mathcal{N}=1$ supersymmetric gauge theories in the case of using the simplest (BRST non-invariant) version of the higher covariant derivative regularization. Consequently, the integrals giving the two-loop $\beta$-function can be reduced to the one-loop integrals giving the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields.