From holography towards real-world nuclear matter

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.