Affinity of NJL${}_2$ and NJL${}_4$ model results on duality and pion condensation in chiral asymmetric dense quark matter

Abstract

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 (${\mu }_B$), isospin (${\mu }_I$) and chiral isospin (${\mu }_{I5}$) chemical potentials. It is shown that the chemical potential ${\mu }_{I5}$ 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 faith 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.

Comments: Proceedings of XXth International Seminar on High Energy Physics, QUARKS-2018