Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in theNJL2model

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 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 $\ensuremath{\mu}$ and chiral charge chemical potential ${\ensuremath{\mu}}_{5}$. 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 $(\ensuremath{\mu},{\ensuremath{\mu}}_{5})$-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.