Scheme-Independent Calculations of Physical Quantities in an ${cal N}=1$ Supersymmetric Gauge Theory

Preprint number: CP3-Origins-2017-23 DNRF90
Authors: Thomas A. Ryttov (CP3-Origins) and Robert Shrock (YITP Stony Brook)

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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 $O(Delta_f^4)$.