Abstract
In this paper we investigate in the large-$N_c$ limit ($N_c$ is the number of colored quarks) the phase structure of a massless (1+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 as well as at nonzero temperature. It is established that chiral isospin chemical potential leads to the generation of charged pion condensation (PC) in dense (nonzero baryon density) and chiral asymmetric quark matter for a wide range of isospin densities. It is shown that there exists a duality correspondence between the chiral symmetry breaking and the charged PC phenomena at any values of temperature even for very hot quark gluon plasma. Moreover, it is shown that charged PC phase with nonzero baryon density can be induced in the model at comparatively high temperatures. This opens up new possible physical systems, where it can be of importance, such as heavy ion collisions, just born neutron stars (proto-neutron stars), supernovas as well as neutron star mergers.
Highlights
Much attention has been paid to the study of dense baryon media with isotopic asymmetry
In this paper the phase structure of the massless NJL2 model (1) with two quark flavors was investigated in the large-Nc limit in the presence of baryon μB, isospin μI and chiral isospin μI5 chemical potentials
The particular case with μI5 1⁄4 0 was solved earlier in Refs. [16,42,43], where it was shown that the toy model (1) does not predict a charged pion condensation (PC) phase of dense and isotopically asymmetric quark matter
Summary
Much attention has been paid to the study of dense baryon (quark) media with isotopic (isospin) asymmetry (different densities of u and d quarks). The effects inherent in real dense quark matter, such as the CSB phenomenon [spontaneous breaking of the continuous axial Uð1Þ symmetry] or charged pion condensation (spontaneous breaking of the continuous isospin symmetry) might be simulated in terms of simpler NJL2-type models, though only in the leading order of the large-Nc approximation Phenomena of real dense quark matter such as the spontaneous breaking of chiral symmetry, the condensation of charged pions and other pairing phenomena in strong magnetic fields can be investigated effectively in the framework of two-dimensional models. The chemical potential μI5 is included in our consideration, because the regions with μI5 ≠ 0 can appear (due to the chiral separation effect) in neutron stars or arise in quark matter formed by the collision of heavy ions just under the influence of a strong magnetic field Some technical details are relegated to Appendices A and B
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