Investigation of the $U_A(1)$ in high temperature QCD on the lattice

In this project we study the effect of the UA(1) anomaly for (2+1)-flavourQCD at high temperature. We apply the overlap operator as a tool to probe thetopological properties of gauge field configurations which have been generatedwithin the Highly Improved Staggered Quark (HISQ) discretization scheme onlattices of size $32^3\times 8$ with $m_l/m_s=1/20$, commonly used for thestudy of QCD thermodynamics. Although we have at present, only results for onevalue of the quark masses and thus cannot monitor the change of the eigenvaluedistributions with the light quark mass, the distribution of the low-lyingeigenvalues of the overlap operator suggests that the $U_A(1)$ is not restoredeffectively even at 1.5 times the pseudo critical temperature. Thecorresponding low-lying eigenmodes show localization properties.