“…Moreover, as reviewed below, in a gauge theory with N ¼ 1 supersymmetry, an exact expression is known for the anomalous dimension of the (gauge-invariant) fermion bilinear operator, and the Taylorseries expansion of this exact expression in powers of Δ f yields κ j coefficients that are all positive. These results led to our conjecture in [13], elaborated upon in our later works, that, in addition to the manifestly positive κ 1 and κ 2 , and our findings in [14][15][16]18] that κ 3 and κ 4 are positive for all of the groups and representations for which we calculated them, (i) the higher-order κ j coefficients with j ≥ 5 are also positive in (vectorial, asymptotically free) nonsupersymmetric gauge theories. In turn, this conjecture led to several monotonicity conjectures, namely that (ii) for fixed s, γψ ψ;IR;Δ s f increases monotonically as N f decreases in the non-Abelian Coulomb phase, and (iii) for fixed N f in the NACP, γψ ψ;IR;Δ s f is a monotonically increasing function of s, so that (iv) for fixed N f in the NACP and for finite s, γψ ψ;IR;Δ s f is a lower bound on the actual anomalous dimension γψ ψ;IR , as defined by the infinite series (2.10).…”