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Register a new userCompetition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL$_2$ model
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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.
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In this paper the duality correspondence between fermion-antifermion and difermion interaction channels is established in two (2+1)-dimensional Gross-Neveu type models with a fermion number chemical potential $mu$ and a chiral chemical potential $mu_5$. The role and influence of this property on the phase structure of the models are investigated. In particular, it is shown that the chemical potential $mu_5$ promotes the appearance of dynamical chiral symmetry breaking, whereas the chemical potential $mu$ contributes to the emergence of superconductivity.
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