Fermi–Einstein condensation in dense QCD-like theories

Abstract

While pure Yang–Mills theories feature the center symmetry, this symmetry is explicitly broken by the presence of dynamical matter. We study the impact of the center symmetry in such QCD-like theories. In the analytically solvable Schwinger model, center transitions take place even under extreme conditions, temperature and/or density, and we show that they are key to the solution of the Silver-Blaze problem. We then develop an effective SU(3) quark model from which colored states are absent under normal conditions by virtue of center sector transitions. The phase diagram is obtained as a function of the temperature and the chemical potential. We show that at low temperatures and intermediate values for the chemical potential the center dressed quarks undergo condensation due to Bose like statistics. This is the Fermi–Einstein condensation. To corroborate the existence of center sector transitions in gauge theories with matter, we study (at vanishing chemical potential) the interface tension in the three-dimensional Z2 gauge theory with Ising matter, the distribution of the Polyakov line in the four-dimensional SU(2)-Higgs model and devise a new type of order parameter which is designed to detect center sector transitions. Our analytical and numerical findings lead us to conjecture a new state of cold, but dense matter in the hadronic phase for which Fermi–Einstein condensation is realized.