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 λR2​=4π/k
for any integer k>1: the minimal S-matrix associated with the Lie algebra
ak−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)/U(1) coset model at level k perturbed
by its first thermal operator.Comment: SWAT-4