  We discuss a relativistic chiral theory of nuclear matter with $\sigma$ and
$\omega$ exchange using a formulation of the $\sigma$ model in which all the
chiral constraints are automatically fulfilled. We establish a relation between
the nuclear response to the scalar field and the QCD one which includes the
nucleonic parts. It allows a comparison between nuclear and QCD information.
Going beyond the mean field approach we introduce the effects of the pion loops
supplemented by the short-range interaction. The corresponding Landau-Migdal
parameters are taken from spin-isospin physics results. The parameters linked
to the scalar meson exchange are extracted from lattice QCD results. These
inputs lead to a reasonable description of the saturation properties,
illustrating the link between QCD and nuclear physics. We also derive from the
corresponding equation of state the density dependence of the quark condensate
and of the QCD susceptibilities.
