Cooper pairing at large N in a two-dimensional model

We study a two-dimensional model of fermi fields ψ that is closely related to the Gross-Neveu model, and show that to leading order in 1/N a 〈ψψ〉 condensate forms. This effect is independent of the chemical potential, a peculiarity that we expect to be specific to two dimensions. We also expect the condensate to be unstable against corrections at higher orders in 1/N. We compute the Greenʹs functions associated with the composite ψψ, and show that the fermion acquires a Majorana mass proportional to the gap, and that a massless Goldstone pole appears.