Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL${}_2$ model

Abstract

We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the (1+1)-dimensional model by Chodos {\it et al.} [ Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature $T$, electric charge chemical potential $\mu$ and chiral charge chemical potential ${\mu }_5$. It is shown that at $G_1<G_2$, where $G_1$ and $G_2$ are the coupling constants in the fermion-antifermion and fermion-fermion channels, the $(\mu ,{\mu }_5)$-phase structure of the model is in a one-to-one correspondence with the phase structure at $G_1>G_2$ (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If $G_1=G_2$, then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.

20 pages, 3 figures; references added; discussion section extended; published version

References in corpus (4)

• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Chiral density waves in the NJL${}_2$ model with quark number and isospin chemical potentials
• Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars
• Dimensional reduction in quantum field theories at finite temperature and density

Cited by in corpus (5)

• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in framework of effective model
• 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
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing