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

TL;DR

This paper demonstrates a new form of the NSVZ relation at the two-loop level in non-Abelian ${ m N}=1$ supersymmetric gauge theories, linking the beta function to anomalous dimensions using higher covariant derivative regularization.

Contribution

It shows that the two-loop NSVZ relation holds with a simple regularization scheme, reducing two-loop integrals to one-loop integrals involving anomalous dimensions.

Findings

Two-loop beta function relates to anomalous dimensions via new NSVZ form.

The relation is verified at two-loop level using higher covariant derivative regularization.

Two-loop integrals can be simplified to one-loop integrals for these theories.

Abstract

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.