Affinity of NJL 2 and NJL 4 model results on duality and pion condensation in chiral asymmetric dense quark matter

In this paper we investigate the phase structure of a (1+1) and (3+1)-dimensional quark model with four-quark interaction and in the presence of baryon ( μ B ), isospin ( μ I ) and chiral isospin ( μ I5 ) chemical potentials. It is shown that the chemical potential μ I5 promotes the appearance of the charged PC phase with nonzero baryon density. Results of both models are qualitatively the same, this fact enhances one's confidence in the obtained predictions. It is established that in the large- N c limit ( N c is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one.