  We review the Sakai-Sugimoto model of holographic QCD at zero temperature and
finite chemical potential, comparing the results to those expected at
large-$N_c$ QCD, and those in a closely related holographic model. We find that
as the baryon chemical potential is increased above a critical value, there is
a phase transition to a nuclear matter phase, the details of which depend on
the model. We argue that the nuclear matter phase is necessarily inhomogeneous
to arbitrarily high density, which suggests an explanation of the "chiral
density wave" instability of the quark Fermi surface in large-$N_c$ QCD. Some
details of the instanton distribution in the holographic dual are reminiscent
of a Fermi surface. This short manuscript summarizes a talk given by M.R. at
"Theory Canada 4" conference, and is based largely (but not entirely) on the
results of \cite{Rozalietal2008}.
