  We consider a chiral baryon-meson model for nucleons and their parity
partners in mirror assignment interacting with pions, sigma and omega mesons to
describe the liquid-gas transition of nuclear matter together with chiral
symmetry restoration in the high density phase. Within the mean-field
approximation the model is known to provide a phenomenologically successful
description of the nuclear-matter transition. Here, we go beyond this
approximation and include mesonic fluctuations by means of the functional
renormalization group. While these fluctuations do not lead to major
qualitative changes in the phase diagram of the model, beyond mean-field, one
is no-longer free to adjust the parameters so as to reproduce the binding
energy per nucleon, the nuclear saturation density, and the nucleon sigma term
all at the same time. However, the prediction of a clear first-order chiral
transition at low temperatures inside the high baryon-density phase appears to
be robust.
