Probing the Infrared Structure of Gauge Theories: A Pade-Approximant Approach

Pade-approximant treatments of the known terms of the QCD $\beta$-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop $\beta$-function contribution. Below this flavour threshold, Pade approximants based upon the QCD $\beta$-function manifest the same infrared attractor structure as that which characterizes the exact NSVZ $\beta$-function of supersymmetric gluodynamics. Such infrared attractor structure is also seen to characterize Pade-approximant treatments of vector SU(N) gauge theory in the large $N$ limit, suggesting common infrared dynamics for the strong and weak phases of this theory.