Topological susceptibility in three-flavor quark-meson model at finite temperature

Abstract

We study ${U}_{A}(1)$ symmetry and its relation to chiral symmetry at finite temperature through the application of the functional renormalization group to the $SU(3)$ quark-meson model. Very different from the mass gap and mixing angel between $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons, which are defined at the mean-field level and behavior like condensates, the topological susceptibility includes a fluctuation-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.