Free energy of hot gauge theories with fermions throughg5

Abstract

We compute the free energy density F for gauge theories, with fermions, at high temperature and zero chemical potential. In the expansion F=${\mathit{T}}^{4}$[${\mathit{c}}_{0}$+${\mathit{c}}_{2}$${\mathit{g}}^{2}$+${\mathit{c}}_{3}$${\mathit{g}}^{3}$+(${\mathit{c}}_{4}^{\ensuremath{'}}$lng+${\mathit{c}}_{4}$)${\mathit{g}}^{4}$+(c $_{5}^{\ensuremath{'}}\mathit{g}$+${\mathit{c}}_{5}$)${\mathit{g}}^{5}$+O(${\mathit{g}}^{6}$)] we determine ${\mathit{c}}_{5}^{\ensuremath{'}}$ and ${\mathit{c}}_{5}$ analytically by calculating two- and three-loop diagrams. The ${\mathit{g}}^{5}$ term constitutes the first correction to the ${\mathit{g}}^{3}$ term and is for the non-Abelian case the last power of g than can be computed within perturbation theory. We find that the ${\mathit{g}}^{5}$ term receives no contributions from overlapping double-frequency sums and that ${\mathit{c}}_{5}^{\ensuremath{'}}$ vanishes. \textcopyright{} 1995 The American Physical Society.