Integrable Marginal Points in the N -Cosine Model

The integrability of the N -cosine model, a N -field generalization of the sine-Gordon model, is investigated. We establish to first order in conformal perturbation theory that, for arbitrary N , the model possesses a quantum conserved current of Lorentz spin 3 on a submanifold of the parameter space where the interaction becomes marginal. The integrability of the model on this submanifold is further studied using renormalization techniques. It is shown that for N= 2, 3, and 4 there exist special points on the marginal manifold at which the N -cosine model is equivalent to models of Gross-Neveu type and therefore is integrable. In the 2-field case we further argue that the points mentioned above exhaust all integrable cases on the marginal submanifold.