  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.
