Sakai-Sugimoto Brane System at High Density

The D4-D8 brane system of Sakai-Sugimoto model at high quark density is studied in the weak coupling regime. We show that the color superconducting phase (for Nc~3) or the chiral density wave (for Nc->infinity) disappears at very large chemical potential, or equivalently at very large compactified dimension that the model possesses. We also comment on the prospects in the strong coupling regime along with the QCD phase diagram.