Competing Condensates in Two Dimensions

We generalize our previous 2-dimensional model in which a pairing condensate psi-psi was generated at large N. In the present case, we allow for both psi-psi and a chiral condensate psibar-psi to exist. We construct the effective potential to leading order in 1/N, and derive the gap equations at finite density and temperature. We study the zero density and temperature situation analytically. We perform the renormalization explicitly and we show that the physics is controlled by a parameter related to the relative strengths of the interactions in the pairing and chiral channels. We show that although a solution to the gap equations exists in which both condensates are non-vanishing, the global minimum of the effective potential always occurs for the case when one or the other condensate vanishes.