Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories

Abstract

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 $gT$. The free energy decomposes into the sum of three terms, corresponding to the momentum scales $T$, $gT$, and $g^{2}T$. 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 $gT/(g^{2}T)$ can be summed up using renormalization group equations.

Comments: 11 pages LaTeX, NUHEP-TH-94-24