The phase diagram of nuclear and quark matter at high baryon density

We review theoretical approaches to explore the phase diagram of nuclear and quark matter at high baryon density. We first look over the basic properties of quantum chromodynamics (QCD) and address how to describe various states of QCD matter. In our discussions on nuclear matter we cover the relativistic mean-field model, the chiral perturbation theory, and the approximation based on the large-N-c limit where N-c is the number of colors. We then explain the liquid gas phase transition and the inhomogeneous meson condensation in nuclear matter with emphasis put on the relevance to quark matter. We commence the next part focused on quark matter with the bootstrap model and the Hagedorn temperature. Then we turn to properties associated with chiral symmetry and exposit theoretical descriptions of the chiral phase transition. There emerge some quark-matter counterparts of phenomena seen in nuclear matter such as the liquid gas phase transition and the inhomogeneous structure of the chiral condensate. The third regime that is being recognized recently is what is called quarkyonic matter, which has both aspects of nuclear and quark matter. We closely elucidate the basic idea of quarkyonic matter in the large-N-c limit and its physics implications. Finally, we discuss some experimental indications for the QCD phase diagram and close the review with outlooks. (C) 2013 Elsevier B.V. All rights reserved.