Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL$_2$ model with baryon-, isospin- and chiral isospin chemical potentials

TL;DR

This paper explores a (1+1)-dimensional quark model revealing a duality between chiral symmetry breaking and charged pion condensation, influenced by various chemical potentials, with implications for phase structure and baryon density.

Contribution

It demonstrates a duality between chiral symmetry breaking and pion condensation in a simplified quark model with multiple chemical potentials.

Findings

Duality exists between chiral symmetry breaking and charged pion condensation.

Chiral isospin chemical potential promotes charged pion condensation with baryon density.

Phase structure is significantly affected by chemical potentials in the large-Nc limit.

Abstract

In this paper we investigate the phase structure of a (1+1)-dimensional schematic 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 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 (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $\mu_{I5}$ promotes the appearance of the charged PC phase with nonzero baryon density.