Comparison of some exact and perturbative results for a supersymmetric SU(N _c) gauge theory

We consider vectorial, asymptotically free N=1 supersymmetric SU(N _c) gauge theories with N _f copies of massless chiral superfields 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 superfield operator product for this purpose. The specific chiral superfield contents that we consider are N _f copies of (i)?F+F̄, (ii)?Adj, (iii)?S ₂+S _̄2, and (iv)?A ₂+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.