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.

11 pages LaTeX, NUHEP-TH-94-24

References in corpus (5)

• The Effective Potential and First-Order Phase Transitions: Beyond Leading Order
• Resummation in a Hot Scalar Field Theory
• The Three-Loop Free Energy for Pure Gauge QCD
• What is Renormalization?
• The Free Energy of Hot QED at Fifth Order

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