The NSVZ relation and the NSVZ scheme for N = 1 non-Abelian supersymmetric theories, regularized by higher covariant derivatives

Abstract

We discuss, how the exact NSVZ -function appears in N = 1 supersymmetric non-Abelian gauge theories, regularized by higher covariant derivatives. In particular, we demonstrate that the renormalization group functions defined in terms of the bare couplings satisfy the NSVZ relation in the case of using this regularization. This occurs, because the loop integrals giving the -function are integrals of double total derivatives with respect to loop momenta. It is also shown that for the renormalization group functions standardly defined in terms of the renormalized couplings the NSVZ scheme can be obtained if the theory is regularized by higher covariant derivatives and only powers of ln/µ are included into the renormalization constants. These statements are confirmed by the explicit calculations in the three-loop approximation, where the scheme dependence is essential.