Topological Susceptibility in Three-Flavor Quark Meson Model at Finite Temperature

We study $U_A(1)$ symmetry and its relation to chiral symmetry at finite temperature through the application of functional renormalization group to the $SU(3)$ quark meson model. Very different from the mass gap and mixing angel between $\eta$ and $\eta'$ mesons which are defined at mean field level and behavior like the chiral condensates, the topological susceptibility includes a fluctuations induced part which becomes dominant at high temperature. As a result, the $U_A(1)$ symmetry is still considerably broken in the chiral symmetry restoration phase.