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Quantum scattering of charged solitons in the complex sine-Gordon model

The scattering of charged solitons in the complex sine-Gordon field theory is investigated. An exact factorizable S-matrix for the theory is proposed when the renormalized coupling constant takes the values $λ^{2}_{R}=4π/k$ for any integer $k>1$: the minimal S-matrix associated with the Lie algebra $a_{k-1}$. It is shown that the proposed S-matrix reproduces the leading semiclassical behaviour of all amplitudes in the theory and is the minimal S-matrix which is consistent with the semiclassical spectrum of the model. The results are completely consistent with the description of the complex sine-Gordon theory as the SU$(2)/{\rm U}(1)$ coset model at level $k$ perturbed by its first thermal operator.