Study of the Renormalization-Group Evolution of ${\cal N}=1$ Supersymmetric Gauge Theories Using Pad\'e Approximants

TL;DR

This paper investigates the renormalization-group flow of ${ m N}=1$ supersymmetric SU($N_c$) gauge theories using Padé approximants to analyze beta functions and compare scheme-dependent results.

Contribution

It introduces a systematic approach using Padé approximants to study the beta functions of supersymmetric gauge theories up to high loop orders, comparing with the NSVZ scheme.

Findings

Padé approximants provide consistent IR zero predictions.

Scheme dependence affects the location of IR zeros and poles.

Results improve understanding of scheme effects in supersymmetric theories.

Abstract

We study asymptotically free SU($N_c$) gauge theories with ${\cal N}=1$ 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 Pad\'e approximants to the beta functions for these theories in the $\overline{\rm DR}$ 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.