Non-renormalization of the Vc¯c-vertices in N=1N=1 supersymmetric theories

Using the Slavnov–Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in N=1N=1 supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regularization. Using the restrictions to the renormalization constants which are imposed by the non-renormalization of the considered vertices we express the exact NSVZ β-function in terms of the anomalous dimensions of the Faddeev–Popov ghosts and of the quantum gauge superfield. In the expression for the NSVZ β-function obtained in this way the contributions of the Faddeev–Popov ghosts and of the matter superfields have the same structure.