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, $\Lambda_q$, and one for gluons, $\Lambda_g$. 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 $\Lambda_q$ and $\Lambda_g$, 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.