Renormalization group, BRST cohomology, and the problem of confinement

Provided the number of matter fields is limited, the structure analysis of the gauge-field propagator results in superconvergence relations which provide a link between long- and short-distance properties of the theory. The information contained in these relations is combined with specific consequences of the Becchi-Rouet-Stora-Tyutin algebra in order to argue for the confinement of transverse gauge-field excitations (gluons) if the number of flavors is less than ten for quantum chromodynamics. With a larger number of matter fields (between ten and sixteen flavors in QCD), confinement is not required. Hence there could be a phase transition. The question of quark confinement is considered only briefly.