Inequalities for QCD functional integrals are used to establish that up to certain technical assumptions. the high temperature chirally restored phase of QCD is effectively symmetric under U(Nf)×U(Nf) rather than SU(Nf)×SU(Nf). If these assumptions are correct, there are no effects due to anomalous breaking of U(1)A on correlation functions in this phase.
@article{arxiv.hep-ph/9601216,
title = {The High Temperature Phase of QCD and {\boldmath $U(1)_A$} Symmetry},
author = {Thomas. D. Cohen},
journal= {arXiv preprint arXiv:hep-ph/9601216},
year = {2010}
}