  We study the Sakai-Sugimoto model of holographic QCD at zero temperature and
finite chemical potential. We find that as the baryon chemical potential is
increased above a critical value, there is a phase transition to a nuclear
matter phase characterized by a condensate of instantons on the probe D-branes
in the string theory dual. As a result of electrostatic interactions between
the instantons, this condensate expands towards the UV when the chemical
potential is increased, giving a holographic version of the expansion of the
Fermi surface. We argue based on properties of instantons that the nuclear
matter phase is necessarily inhomogeneous to arbitrarily high density. This
suggests an explanation of the "chiral density wave" instability of the quark
Fermi surface in large N_c QCD at asymptotically large chemical potential. We
study properties of the nuclear matter phase as a function of chemical
potential beyond the transition and argue in particular that the model can be
used to make a semi-quantitative prediction of the binding energy per nucleon
for nuclear matter in ordinary QCD.
