Effective fermion masses of order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>gT</mml:mi></mml:math>in high-temperature gauge theories with exact chiral invariance

Abstract

It is shown that, at finite temperature, chiral invariance does not imply that fermion propagators have poles at ${K}^{2}=0$. Instead, a zero-momentum fermion has energy ${K}^{0}=M$, where ${M}^{2}=\frac{{g}^{2}C(R){T}^{2}}{8}$ and $C(R)$ is the quadratic Casimir of the fermion representation. The dispersion relation for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}\ensuremath{\ne}0$ is computed and can be crudely approximated (to within 10%) by ${K}^{0}\ensuremath{\approx}{({M}^{2}+{\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}}^{2})}^{\frac{1}{2}}$. Applications to high-temperature QCD, SU(2)\ifmmode\times\else\texttimes\fi{}U(1), and grand unified theories are discussed.