Integrable Marginal Points in the N-Cosine Model

TL;DR

This paper investigates the integrability of the N-cosine model, identifying conditions under which it possesses conserved currents and is equivalent to integrable models like Gross-Neveu, especially for N=2, 3, and 4.

Contribution

It establishes the existence of quantum conserved currents in the N-cosine model and identifies specific points where the model is integrable and equivalent to known integrable models.

Findings

Existence of a quantum conserved current of Lorentz spin 3 on a marginal submanifold.

For N=2, 3, 4, the model is equivalent to integrable Gross-Neveu type models.

All integrable cases for N=2 are identified on the marginal submanifold.

Abstract

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.