Abstract
We study su(3) Toda field theory with a pure imaginary coupling constant. Using an analysis of semi-classical soliton solutions and assuming quantum group su q (3) symmetry in the theory, we construct its relativistic factorizable S-matrix. At special values of the coupling constant these S-matrices, which satisfy the unitary condition, are consistent and their N-body Hilbert space must be restricted. These features agree with the prediction from the perturbation theory of W 3 minimal unitary CFTs.
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