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

TL;DR

The paper addresses the problem of finding an exact, factorizable S-matrix for the complex sine-Gordon theory of charged solitons. By analyzing the semiclassical spectrum and soliton solutions, the authors propose a minimal, diagonal S-matrix based on the $a_{k-1}$ algebra at the renormalized coupling $λ_R^2=4π/k$ and validate it against meson-soliton and soliton-soliton scattering data. They show that the S-matrix reproduces leading semiclassical phase shifts and the positions/residues of poles, and that the charges must be identified modulo $k$, consistent with a coset description in terms of SU(2)/U(1) at level $k$ and a ${f Z}_k$ parafermion structure. The work thus provides a strong candidate for the exact solution of the CSG model in this coupling class and links the integrable structure to perturbed coset CFTs and gauged WZW constructions.

Abstract

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.