arXiv subjects
Publications and source records attributed to C. G. North.
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 $3N_c/2 < N_f < 3N_c$.
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.
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 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.