Effective fermion masses of order gT in high-temperature gauge theories with exact chiral invariance

It is shown that, at finite temperature, chiral invariance does not imply that fermion propagators have poles at K²=0. Instead, a zero-momentum fermion has energy K⁰=M, where M²=g²C(R)T²8 and C(R) is the quadratic Casimir of the fermion representation. The dispersion relation for K-->≠0 is computed and can be crudely approximated (to within 10%) by K⁰~(M²+K-->²)¹². Applications to high-temperature QCD, SU(2)×U(1), and grand unified theories are discussed.