  Quantum chromodynamics is notoriously difficult to solve at nonzero baryon
density, and most models or effective theories of dense quark or nuclear matter
are restricted to a particular density regime and/or a particular form of
matter. Here we study dense (and mostly cold) matter within the holographic
Sakai-Sugimoto model, aiming at a strong-coupling framework in the wide density
range between nuclear saturation density and ultra-high quark matter densities.
The model contains only three parameters, and we ask whether it fulfills two
basic requirements of real-world cold and dense matter, a first-order onset of
nuclear matter and a chiral phase transition at high density to quark matter.
Such a model would be extremely useful for astrophysical applications because
it would provide a single equation of state for all densities relevant in a
compact star. Our calculations are based on two approximations for baryonic
matter, firstly an instanton gas and secondly a homogeneous ansatz for the
non-abelian gauge fields on the flavor branes of the model. While the instanton
gas shows chiral restoration at high densities but an unrealistic second-order
baryon onset, the homogeneous ansatz behaves exactly the other way around. Our
study thus provides all ingredients that are necessary for a more realistic
model and allows for systematic improvements of the applied approximations.
