Integrable boundary interaction in 3D target space: The "pillow-brane" model

We propose a model of boundary interaction, with three-dimensional target space, and the boundary values of the field X∈R³ constrained to lay on a two-dimensional surface of the "pillow" shape. We argue that the model is integrable, and suggest that its exact solution is described in terms of certain linear ordinary differential equation.

The expansion in terms of the local IM appears in integrable boundary theories which flow down to the "basic" boundary fixed point, the one which admits no primary boundary fields but the identity operator. In those theories the expansion in I_s corresponds to expansion of the infrared effective action in terms of descendants of the identity. Clearly, the Dirichlet boundary is of that kind.