Free energy of QCD at high temperature.

Effective-field-theory methods are used to separate the free energy for a nonabelian 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 3-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.