Scheme dependence and the NSVZ $β$-function

Abstract

We investigate the connection between the NSVZ and the DRED forms of the gauge $β$-function in an $N=1$ supersymmetric gauge theory. We construct a coupling constant redefinition that relates the two forms up to four loops. By abelian calculations, we are able to infer the complete non-abelian form of $β_g^{(3)DRED}$, and also $β_g^{(4)DRED}$ except for one undetermined parameter.