Study of the Renormalization-Group Evolution of $\mathcal{N}=1$ Supersymmetric Gauge Theories Using Padé Approximants

Abstract

We study asymptotically free SU($N_c$) gauge theories with $\mathcal{N}=1$ 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 $\overline{\mathrm{DR}}$ 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.

17 pages latex

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Cited by in corpus (11)

• Higher-Order Scheme-Independent Series Expansions of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ in Conformal Field Theories
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Consistent Perturbative Fixed Point Calculations in QCD and SQCD
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory