TEMPERATURE-DEPENDENCE OF THE QCD COUPLING

We present a one-loop calculation of a gauge invariant QCD beta-functi on. Using both momentum and temperature renormalization group equation s we investigate the running coupling in the magnetic sector as a func tion of temperature and momentum scale. At fixed momentum scale we fin d that, in contrast to lambdaphi4 or QED, high temperature QCD is stro ngly coupled, even after renormalization group improvement. However, i f the momentum scale is changed simultaneously with temperature in a s pecified manner, the coupling decreases. We also point out in what reg ime dimensional reduction occurs. Both the cases N(f) smaller and larg er than 11/2N(c) are discussed.