Preprint number: CP3-Origins-2017-23 DNRF90

Authors:

We consider an asymptotically free, vectorial, ${cal N}=1$ supersymmetric

gauge theory with gauge group $G$ and $N_f$ pairs of chiral superfields in

the respective representations ${cal R}$ and $bar {cal R}$ of $G$, having

an infrared fixed point (IRFP) of the renormalization group at

$alpha_{IR}$. We present exact results for the anomalous dimensions of

various (gauge-invariant) composite chiral superfields $gamma_{{Phi}_{rm

prod}}$ at the IRFP and prove that these increase

monotonically with decreasing $N_f$ in the non-Abelian Coulomb phase of the

theory and that scheme-independent expansions for these anomalous dimensions

as powers of an $N_f$-dependent variable, $Delta_f$, exhibit monotonic and

rapid convergence to the exact $gamma_{{Phi}_{rm prod}}$ throughout this

phase. We also present a

scheme-independent calculation of the derivative of the beta function,

$dbeta/dalpha |_{alpha=alpha_{IR}}$, denoted $beta’_{IR}$, up to

$O(Delta_f^3)$ for general $G$ and ${cal R}$, and, for the case

$G={rm SU}(N_c)$, ${cal R}=F$, we give an analysis of the properties of

$beta’_{IR}$ calculated to $O(Delta_f^4)$.