a General Effective Theory for Dense Quark Matter

A general effective action for quark matter at nonzero temperature and/or nonzero density is derived. Irrelevant quark modes are distinguished from relevant quark modes, and hard from soft gluon modes, by introducing two separate cut-offs in momentum space, one for quarks, Λ_q, and one for gluons, Λ_g. Irrelevant quark modes and hard gluon modes are then exactly integrated out in the functional integral representation of the QCD partition function. Depending on the specific choice for Λ_q and Λ_g, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the "Hard Thermal Loop" (HTL) or the "Hard Dense Loop" (HDL) action, as well as the high-density effective theory proposed by Hong and others.