Integrable marginal points in the N-cosine model

The integrability of the N-cosine model, an 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 paints on the marginal manifold at which the N-cosine model is equivalent to models of the 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. (C) 2000 Elsevier Science B.V. All rights reserved.