Dense Hadronic Matter in Holographic QCD

We provide a method to study hadronic matter at finite density in the context of the Sakai-Sugimoto. We introduce the baryon chemical potential through the external U(1)_v in the induced (DBI plus CS) action on the D8-probe-brane, where baryons are skyrmions. Vector dominance is manifest at finite density. We derive the baryon density effect on the energy density, the dispersion relations of pion and vector meson at large N_c. The energy density asymptotes a constant at large density suggesting that dense matter at large N_c freezes, with the pion velocity dropping to zero. Holographic dense matter enforces exactly the tenets of vector dominance, and screens efficiently vector mesons. At the freezing point the \rho-\pi\pi coupling vanishes with a finite rho mass of about 20% its vacuum value