NONLINEAR SIGMA MODELS ON A HALF PLANE

Abstract

In the context of integrable field theory with boundary, the integrable nonlinear sigma models in two dimensions, for example the O(N), the principal chiral, the CPN−1 and the complex Grassmannian sigma models, are discussed on a half plane. In contrast to the well-known cases of sine-Gordon, nonlinear Schrödinger and affine Toda field theories, these nonlinear sigma models in two dimensions are not classically integrable if restricted on a half plane. It is shown that the infinite set of nonlocal charges characterizing the integrability on the whole plane is not conserved for the free (Neumann) boundary condition. If we require that these nonlocal charges be conserved, then the solutions become trivial.