The fate of axial anomaly in high temperature QCD

The axial anomaly is believed to affect the order of phase transition
related to chiral symmetry restoration in QCD with two light quark
flavours.  I discuss about our recent study on the effects of the
axial anomaly(U_A(1)) for 2+1-flavour QCD at high temperature. We
apply the overlap Dirac operator as a tool to probe the topological
properties of gauge field configurations which have been generated
within the Highly Improved Staggered Quark (HISQ) discretization
scheme on different lattice sizes, commonly used for the study of QCD
thermodynamics. The distribution of the low-lying eigenvalues of the
overlap operator suggests that the U_A(1) is not restored effectively
even at 1.5 times the pseudo critical temperature, corresponding to
the restoration of chiral symmetry. I will discuss possible
implications of our study for the phase diagram of QCD. Our study also
suggest that the high temperature phase of QCD can be described as a
dilute gas of instantons.