We calculate the three loop gauge β-function for an abelian N = 1 supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ β-function, and by generalising this redefinition to the non-abelian case we derive the DRED three loop gauge β-function for the non-abelian case.

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

We calculate the three loop anomalous dimension for a general N = 1 supersymmetric gauge theory. The result is used to probe the possible existence of renormalisation invariant relationships between the Yukawa and gauge couplings.

We present calculations of the leading and O(1/N f ) terms in a large-N f expansion of the β-functions and anomalous dimensions for various supersymmetric gauge theories, including supersymmetric QCD. In the case of supersymmetric QCD, we show that our O(1/N f ) approximation displays an infra-red fixed point in the conformal window 3 2