As a first step towards a realistic phenomenological description of vector and axial-vector mesons in nuclear matter, we calculate the spectral functions of the $��$ and the $a_1$ meson in a chiral baryon-meson model as a low-energy effective realization of QCD, taking into account the effects of fluctuations from scalar mesons, nucleons, and vector mesons within the Functional Renormalization Group (FRG) approach. The phase diagram of the effective hadronic theory exhibits a nuclear liquid-gas phase transition as well as a chiral phase transition at a higher baryon-chemical potential. The in-medium $��$ and $a_1$ spectral functions are calculated by using the previously introduced analytically-continued FRG (aFRG) method. Our results show strong modifications of the spectral functions in particular near the critical endpoints of both phase transitions which may well be of relevance for electromagnetic rates in heavy-ion collisions or neutrino emissivities in neutron-star merger events.

16 pages, 10 figures