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

TL;DR

This paper proposes an exact S-matrix for charged soliton scattering in the complex sine-Gordon model, aligning with semiclassical results and the SU(2)/U(1) coset structure at specific coupling values.

Contribution

It introduces a minimal, factorizable S-matrix for the complex sine-Gordon model at certain couplings, consistent with semiclassical and coset model descriptions.

Findings

Proposes an exact S-matrix for charged solitons.

Shows the S-matrix matches semiclassical amplitudes.

Connects the model to the SU(2)/U(1) coset at level k.

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 $\lambda^{2}_{R}=4\pi/k$ 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.