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 $\eta$ and ${\eta }^{\prime }$ 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.

• Received 21 November 2015

DOI:https://doi.org/10.1103/PhysRevD.93.074006