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Boundary scattering, symmetric spaces and the principal chiral model on the half-line

N. J. MacKay·B. J. Short
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Abstract

We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H x G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H x G/H, which correspond to our boundary conditions.

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N. J. MacKay, B. J. Short. 2003-07-29. Boundary scattering, symmetric spaces and the principal chiral model on the half-line. https://doi.org/10.1007/s00220-002-0735-y

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