Supersymmetry, quantum corrections, and the higher derivative regularization

Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

^* e-mail: stepan@m9com.ru 1For a recent discussion see Ref. [6].

Published online: 31 October 2018

Abstract

We investigate the structure of quantum corrections in N = 1 supersymmetric theories using the higher covariant derivative method for regularization. In particular, we discuss the non-renormalization theorem for the triple gauge-ghost vertices and its connection with the exact NSVZ β-function. Namely, using the finiteness of the triple gauge-ghost vertices we rewrite the NSVZ equation in a form of a relation between the β-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the matter superfields. We argue that it is this form that follows from the perturbative calculations, and give a simple prescription how to construct the NSVZ scheme in the non-Abelian case. These statements are confirmed by an explicit calculation of the three-loop contributions to the β-function containing Yukawa couplings. Moreover, we calculate the two-loop anomalous dimension of the ghost superfields and demonstrate that for doing this calculation it is very important that the quantum gauge superfield is renormalized non-linearly.