Topological Charge and $U(1{)}_A$ Symmetry in the High Temperature Phase of QCD

Abstract

We discuss the global symmetries of the high temperature phase of QCD with $N_f$ massless quarks. We show that the $U(N_f)\times U(N_f)$ symmetries are only violated by operators of dimension $\ge 3N_f$. For $N_f>2$ this implies that the thermal two-point correlation functions of the ${\eta }^{\prime }$ and ${\pi }^a$'s are identical. We discuss the implications of this for the chiral phase transition at finite temperature.

Comments: 8 pages, LaTeX