  We address the connection between the saturating behavior of infinite nuclear
matter and the description of finite nuclei based on state-of-the-art chiral
two- and three-nucleon forces. We observe that chiral two- and three-nucleon
interactions (at N2LO and at N3LO) which have been found to predict realistic
binding energies and radii for a wide range of finite nuclei (from p-shell
nuclei up to nickel isotopes) are unable to saturate infinite nuclear matter.
On the other hand, it has been shown that, when the fits of the cD and cE
couplings of the chiral three-nucleon interactions include the constraint of
nuclear matter saturation in addition to, as is typically the case, the triton
binding energy, medium-mass nuclei are underbound and their radii are
sytematically too large. We discuss this apparent inconsistency and perform
test calculations for various scenarios to shed light on the issue.
