Comparative study of criticality conditions for anomalous dimensions using exact results in an N=1 supersymmetric gauge theory

Two of the conditions that have been suggested to determine the lower boundary of the conformal window in asymptotically free gauge theories are the linear condition, gamma psi psi;IR = 1, and the quadratic condition, gamma psi psi;IR(2 - gamma psi psi;IR) = 1, where gamma psi psi;IR is the anomalous dimension of the operator psi psi at an infrared fixed point in a theory. We compare these conditions as applied to an N = 1 supersymmetric gauge theory with gauge group G and Nf pairs of massless chiral superfields phi and phi similar to transforming according to the respective representations R and R of G. We use the fact that gamma psi psi;IR and the value Nf = Nf;cr at the lower boundary of the conformal window are both known exactly for this theory. In contrast to the case with a nonsupersymmetric gauge theory, here we find that in higher-order calculations, the linear condition provides a more accurate determination of Nf;cr than the quadratic condition when both are calculated to the same finite order of truncation in a scheme-independent expansion.