Effective Theories of Dense and Very Dense Matter

The exploration of the phase diagram of dense baryonic matter is an area of intense theoretical and experimental activity. Baryonic systems, from dilute neutron matter at low density to superconducting quark matter at high density, exhibit an enormous variety of many-body effects. Despite its simplicity all these phenomena are ultimately described by the lagrangian of QCD. In practice it is usually very difficult to describe QCD many-body systems directly in terms of the QCD lagrangian, and even in cases where this is possible it is often not the most convenient and most transparent description. Instead, it is advantageous to employ an effective field theory (EFT) formulated in terms of the relevant degrees of freedom. EFTs also provide a unified description of physical systems involving very different length scales, such as Fermi liquids in nuclear and atomic physics, or non-Fermi liquid gauge theories involving colored quarks or charged electrons. In these lectures we shall discuss the many body physics of several effective field theories relevant to the structure of hadronic matter. We will concentrate on two regimes in the phase diagram. At low baryon density the relevant degrees of freedom are neutrons and protons, while at very high baryon density the degrees of freedom are quarks and gluons. These lectures do not provide an introduction to effective field theories (see [1, 2, 3]), nor an exhaustive treatment of many body physics (see [4, 5, 6]) or the physics of dense quark matter (see [7, 8]).