Dense hadronic matter in holographic QCD

We provide a method to study hadronic matter at finite density in the context of the Sakai-Sugimoto model. We introduce the baryon chemical potential through the external U(1)_v gauge field 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 effect of the baryon density on the energy density, and on the dispersion relations of pions and vector mesons at large N _c. The energy density asymptotes are 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 efficiently screens vector mesons. At the freezing point, the ρ - ππ coupling vanishes with a finite rho mass of about 20% its vacuum value.