On the sine-Gordon--Thirring equivalence in the presence of a boundary

TL;DR

This paper explores the connection between the sine-Gordon and Thirring models with boundaries, providing the reflection R-matrix and relating boundary parameters to known formal parameters, advancing understanding of boundary integrability.

Contribution

It establishes the boundary correspondence between the sine-Gordon and Thirring models and derives the reflection R-matrix for the massive Thirring model.

Findings

Derived the reflection R-matrix for the boundary Thirring model.

Clarified the relationship between boundary parameters and Ghoshal-Zamolodchikov parameters.

Connected boundary conditions in sine-Gordon and Thirring models.

Abstract

In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection $R$-matrix for the massive Thirring model, which is related to the physical boundary parameters of the sine-Gordon model, is given. The relationship between the the boundary parameters and the two formal parameters appearing in the work of Ghoshal and Zamolodchikov is discussed.