Topological charge and U(1)A symmetry in the high temperature phase of QCD

We discuss the global symmetries of the high temperature phase of QCD with Nf massless quarks. We show that the U(Nf) × U(Nf) symmetries are only violated by operators of dimension ≥ 3Nf. For Nf > 2 this implies that the thermal two-point correlation functions of the η′ and πaʹs are identical. We discuss the implications of this for the chiral phase transition at finite temperature.