Free energy of QCD at high temperature

Effective-field-theory methods are used to separate the free energy for a non-Abelian gauge theory at high temperature T into the contributions from the momentum scales T, gT, and g(2)T, where g is the coupling constant at the scale 2 pi T. The effects of the scale T enter through the coefficients in the effective Lagrangian for the three-dimensional effective theory obtained by dimensional reduction. These coefficients dan be calculated as power series in g(2). The contribution to the free energy from the scale gT can be calculated using perturbative methods in the effective theory. It can be expressed as an expansion in g Starting at order g(3). The contribution from the scale g(2)T must be calculated using nonperturbative methods, but nevertheless it can be expanded in powers of g beginning at order g(6). We calculate the free energy explicitly to order g(5). We also outline the calculations necessary to obtain the free energy to order g(6).