FREE-ENERGY OF QCD AT HIGH-TEMPERATURE

Effective-field-theory methods are used to separate the free energy fo r a non-Abelian gauge theory at high temperature T into the contributi ons 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 throug h the coefficients in the effective Lagrangian for the three-dimension al effective theory obtained by dimensional reduction. These coefficie nts dan be calculated as power series in g(2). The contribution to the free energy from the scale gT can be calculated using perturbative me thods 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 b e calculated using nonperturbative methods, but nevertheless it can be expanded in powers of g beginning at order g(6). We calculate the fre e energy explicitly to order g(5). We also outline the calculations ne cessary to obtain the free energy to order g(6).