  We investigate meson and nucleon dynamics at finite baryon density and
temperature by coupling the nucleon field and the omega meson to the
three-flavor linear sigma model and calculate hadronic properties around the
nuclear liquid-gas transition. We apply the functional renormalization group
method, and find that mesonic fluctuations increase the strength of the
coefficient of the $U_A(1)$ breaking determinant operator as a function of the
chiral condensate. As a consequence, we find that the actual value of the
anomaly increases discontinuously at the first order nuclear liquid-gas
transition. We calculate how mesonic masses and partial restoration of chiral
symmetry are modified due to such an effect.
