The Free Energy of Hot Gauge Theories with Fermions Through

We compute the free energy density F for gauge theories, with fermions, at high temperature and zero chemical potential. In the expansion F = T [c0 + c2g 2 + c3g 3 + (c4 ln g + c4)g + (c5 ln g+ c5)g +O(g)], we determine c5 and c5 analytically by calculating twoand three-loop diagrams. The g term constitutes the first correction to the g term and is for the non-Abelian case the last power of g that can be computed within perturbation theory. We find that the g term receives no contributions from overlapping double-frequency sums and that c5 vanishes.