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

Abstract

We consider an asymptotically free, vectorial, $\mathcal{N}=1$ supersymmetric gauge theory with gauge group $G$ and $N_f$ pairs of chiral superfields in the respective representations $\mathcal{R}$ and $\bar{\mathcal{R}}$ 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 ${\gamma }_{{\Phi }_{\mathrm{prod}}}$ 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 ${\gamma }_{{\Phi }_{\mathrm{prod}}}$ throughout this phase. We also present a scheme-independent calculation of the derivative of the beta function, $d\beta /d\alpha {|}_{\alpha ={\alpha }_{IR}}$, denoted ${\beta }_{IR}^{\prime }$, up to $O({\Delta }_f^3)$ for general $G$ and $\mathcal{R}$, and, for the case $G=\mathrm{SU}(N_c)$, $\mathcal{R}=F$, we give an analysis of the properties of ${\beta }_{IR}^{\prime }$ calculated to $O({\Delta }_f^4)$.

Comments: 29 pages, 13 figures