Supersymmetric Sine-Gordon Model and the Eight-Vertex Free Fermion model with Boundary

TL;DR

This paper computes boundary scattering amplitudes in the supersymmetric sine-Gordon model and solves the boundary Yang-Baxter equation for the eight-vertex free fermion model, linking boundary parameters with scattering data.

Contribution

It introduces a dual approach to relate boundary parameters in supersymmetric sine-Gordon and free fermion models, providing explicit boundary reflection matrices.

Findings

Boundary scattering amplitudes for breathers computed.

Boundary Yang-Baxter equation solved for eight-vertex model.

Bulk S-matrices identified with trigonometric limit of Boltzmann weights.

Abstract

We compute the boundary scattering amplitudes of the breathers of the supersymmetric sine-Gordon model using the fusion of the soliton-antisoliton pair scattering with the boundary with a known result of the soliton boundary scattering amplitudes. We also solve the boundary Yang-Baxter equation of the eight-vertex free fermion models to find the boundary reflection matrices. The former result is confirmed by the latter since the bulk $S$-matrices of the breathers can be identified with the trigonometric limit of the Boltzmann weights of the free fermion models. Our dual approach can answer a few quesions on the relationships between the free parameters in the boundary potential and those in the scattering amplitudes.