Study of the renormalization-group evolution of $\mathcal{N}=1$ supersymmetric gauge theories using Pad\'e approximants

Study of the renormalization-group evolution of $N = 1$ supersymmetric gauge theories using Padé approximants

Gongjun Choi and Robert Shrock

Phys. Rev. D 93, 065013 – Published 7 March 2016

Abstract

We study asymptotically free $SU (N_{c})$ gauge theories with $N = 1$ supersymmetry, including the purely gluonic theory and theories with $N_{f}$ copies of a pair of massless chiral superfields in the respective representations $R$ and $\bar{R}$ of $SU (N_{c})$ . The cases in which $R$ is the fundamental representation and the symmetric and antisymmetric rank-2 tensor representation are considered. We calculate Padé approximants to the beta functions for these theories in the $\bar{DR}$ scheme up to four-loop order for the gluonic theory and up to three-loop order for the theories with matter superfields and compare results for IR zeros and poles with results from the NSVZ beta function. Our calculations provide a quantitative measure, for these theories, of how well finite-order perturbative results calculated in one scheme reproduce properties of a known beta function calculated in a different scheme.