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We establish a holographic bottom-up model which covers both the baryonic andquark matter phases in cold and dense QCD. This is obtained by including thebaryons using simple approximation schemes in the V-QCD model, which alsoincludes the backreaction of the quark matter to the dynamics of pureYang-Mills. We examine two approaches for homogeneous baryon matter: baryons asa thin layer of noninteracting matter in the holographic bulk, and baryons witha homogeneous bulk gauge field. We find that the second approach exhibitsphenomenologically reasonable features. At zero temperature, the vacuum,baryon, and quark matter phases are separated by strongly first ordertransitions as the chemical potential varies. The equation of state in thebaryonic phase is found to be stiff, i.e., the speed of sound clearly exceedsthe value $c_s^2=1/3$ of conformal plasmas at high baryon densities.

Cool baryon and quark matter in holographic QCD