Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories

Eric Braaten
1995 Physical Review Letters  
The free energy of a nonabelian gauge theory at high temperature T can be calculated to order g^5 using resummed perturbation theory, but the method breaks down at order g^6. A new method is developed for calculating the free energy to arbitrarily high accuracy in the high temperature limit. It involves the construction of a sequence of two effective field theories by first integrating out the momentum scale T and then integrating out the momentum scale g T. The free energy decomposes into the
more » ... um of three terms, corresponding to the momentum scales T, gT, and g^2T. The first term can be calculated as a perturbation series in g^2(T), where g(T) is the running coupling constant. The second term in the free energy can be calculated as a perturbation series in g(T), beginning at order g^3. The third term can also be expressed as a series in g(T) beginning at order g^6, with coefficients that can be calculated using lattice simulations of 3-dimensional QCD. Leading logarithms of T/(gT) and of gT/(g^2T) can be summed up using renormalization group equations.
doi:10.1103/physrevlett.74.2164 pmid:10057859 fatcat:z2z5x57ntjbp7mxadgst5276dq