Anomaly matching in QCD thermal phase transition

Abstract

We study an ’t Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a ℤ 2 symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the ℤ 2 symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly before and after QCD phase transition. The effect of the imaginary chemical potential is suppresssed in the large N expansion, and we discuss implications of the ’t Hooft anomaly matching for the nature of QCD phase transition with and without the imaginary chemical potential. Arguments based on universality alone are disfavored, and a first order phase transition may be the simplest possibility if the large N expansion is qualitatively good.