Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing

Abstract

The massless Gross-Neveu and chiral Gross-Neveu models are well known examples of integrable quantum field theories in 1+1 dimensions. We address the question whether integrability is preserved if one either replaces the four-fermion interaction in fermion-antifermion channels by a dual interaction in fermion-fermion channels, or if one adds such a dual interaction to an existing integrable model. The relativistic Hartree-Fock-Bogoliubov approach is adequate to deal with the large N limit of such models. In this way, we construct and solve three integrable models with Cooper pairing. We also identify a candidate for a fourth integrable model with maximal kinematic symmetry, the "perfect" Gross-Neveu model. This type of field theories can serve as exactly solvable toy models for color superconductivity in quantum chromodynamics.

16 pages, 4 figures

References in corpus (6)

• Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Tricritical behavior of the massive chiral Gross-Neveu model
• Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL${}_2$ model
• Baryons in the large N limit of the massive two-dimensional Nambu-Jona-Lasinio model
• Exact solution of N baryon problem in the Gross-Neveu model

Cited by in corpus (6)

• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ 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
• Gross-Neveu model with O(2)${}_L\times$O(2)${}_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
• Dark solitons of the Gross-Neveu model
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation