Non-Linear Sigma Models on a Half Plane

Details Non-Linear Sigma Models on a Half Plane Non-Linear Sigma Models on a Half Plane

1995-09-27

arxiv.org/abs/hep-th/9509153v1

Int.J.Mod.Phys. A11 (1996) 3127-3144

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, latex, no figures

Scientific paper

In the context of integrable field theory with boundary, the integrable non-linear sigma models in two dimensions, for example, the $O(N)$, the principal chiral, the ${\rm CP}^{N-1}$ and the complex Grassmannian sigma models are discussed on a half plane. In contrast to the well known cases of sine-Gordon, non-linear Schr\"odinger and affine Toda field theories, these non-linear sigma models in two dimensions are not classically integrable if restricted on a half plane. It is shown that the infinite set of non-local charges characterising the integrability on the whole plane is not conserved for the free (Neumann) boundary condition. If we require that these non-local charges to be conserved, then the solutions become trivial.

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