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 g²T, where g is the coupling constant at the scale 2πT. 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 can be calculated as power series in g². 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 g³. The contribution from the scale g²T must be calculated using nonperturbative methods, but nevertheless it can be expanded in powers of g beginning at order g⁶. We calculate the free energy explicitly to order g⁵. We also outline the calculations necessary to obtain the free energy to order g⁶.