Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory

TL;DR

This paper compares perturbative and exact results for the conformal window in supersymmetric SU(N_c) gauge theories with various matter representations, finding that perturbation slightly overestimates the lower boundary of conformality.

Contribution

It provides a detailed comparison between perturbative predictions and exact results for the conformal phase boundary in supersymmetric gauge theories with different matter content.

Findings

Perturbative results slightly overestimate the lower boundary of the conformal window.

Perturbation underestimates the size of the conformal interval in N_f.

Results quantify the accuracy of perturbative methods in supersymmetric gauge theories.

Abstract

We consider vectorial, asymptotically free ${\cal N}=1$ supersymmetric SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of $N_f$, compare with exact results. We make use of two-loop and three-loop calculations of the beta function and anomalous dimension of the quadratic chiral super field operator product for this purpose. The specific chiral superfield contents that we consider are $N_f$ copies of (i) $F+\bar F$, (ii) $Adj$, (iii) $S_2+\bar S_2$, and (iv) $A_2 + \bar A_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of $N_{f,cr}$ relative to the respective exact results for these representations, i.e., slightly underestimate the interval in $N_f$ for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories.