Looking for $U(1)_A$ Restoration in Hot QCD with Domain Wall Fermions

The effects of the axial anomaly are suppressed at high temperatures due to screening effects in the quark-gluon plasma. If the suppression is nearly complete close to the chiral transition temperature, this can have consequences for the nature of the phase transition. The use of a chiral action such as Domain Wall Fermions allows us to gain a deeper insight into the issue. Our lattice sizes were $16^3\times 8\times L_s$, with $L_s=32$ or 48, and our pion mass was approximately 200 MeV. We found that $U(1)_A$ stayed broken above the chiral transition. However the breaking was found to be due to topologically nontrivial configurations which raises the question as to whether it persists in the thermodynamic limit. We also present results for the eigenvalue density of the Dirac operator. It is seen that although the density decreases dramatically across the chiral transition temperature, $U(1)_A$ still remains broken at our current volume and quark mass due to the presence of zero modes.