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 ${\cal N}=1$ 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.Comment: 12 pages, 3 figures, the version accepted for publication in Physics Letters

Exact renormalization of the photino mass in softly broken N=1{\cal N}=1 SQED with NfN_f flavors regularized by higher derivatives

We consider the softly broken ${\cal N}=1$ supersymmetric electrodynamics, regularized by higher derivatives. For this theory we demonstrate that the renormalization of the photino mass is determined by integrals of double total derivatives in the momentum space in all orders. Consequently, it is possible to derive the NSVZ-like exact relation between the photino mass anomalous dimension and the anomalous dimension of the matter superfields in the rigid theory by direct summation of supergraphs. It is important that both these renormalization group functions are defined in terms of the bare coupling constant, so that the considered NSVZ-like relation is valid independently of the subtraction scheme in the case of using the higher derivative regularization. The factorization of integrals defining the photino mass renormalization into integrals of double total derivatives is verified by an explicit two-loop calculation.Comment: 32 pages, 8 figures; the version accepted for publication in JHE

Universal invariant renormalization of supersymmetric Yang-Mills theory

A manifestly invariant renormalization scheme of N=1 nonabelian supersymmetric gauge theories is proposed.Comment: LaTeX, 14 pages, 2 eps figure