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The massless Gross-Neveu and chiral Gross-Neveu models are well knownexamples of integrable quantum field theories in 1+1 dimensions. We address thequestion whether integrability is preserved if one either replaces thefour-fermion interaction in fermion-antifermion channels by a dual interactionin fermion-fermion channels, or if one adds such a dual interaction to anexisting integrable model. The relativistic Hartree-Fock-Bogoliubov approach isadequate to deal with the large N limit of such models. In this way, weconstruct and solve three integrable models with Cooper pairing. We alsoidentify a candidate for a fourth integrable model with maximal kinematicsymmetry, the "perfect" Gross-Neveu model. This type of field theories canserve as exactly solvable toy models for color superconductivity in quantumchromodynamics.

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