Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories

Perturbative calculations of the free energy of a non-Abelian gauge theory at high temperature T break down at order g^6. This problem is solved by constructing a sequence of two effective field theories in which the momentum scales T and gT are integrated out. The free energy is decomposed into contributions from the momentum scales T, gT, and g^2T. The three terms are a power series in g^2, a power series in g beginning at order g^3, and a power series in g beginning at order g^6. In the g^2T contribution, the coefficients in the power series can be calculated using lattice simulations of 3-dimensional QCD. Renormalization group equations can be used to sum up the leading logarithms of T/ (gT) and of gT/ (g^2T).