On duality and reflection factors for the sinh-Gordon model

TL;DR

This paper investigates the duality and reflection factors in the sinh-Gordon model with boundary conditions, analyzing perturbative results and their relation to sine-Gordon models, with implications for boundary parameterizations.

Contribution

It demonstrates a dual relationship between sinh-Gordon and sine-Gordon boundary models and verifies Ghoshal's reflection factor formula perturbatively at the lightest breather level.

Findings

Perturbative check of Ghoshal's formula at O(β²)

Duality between sinh-Gordon and sine-Gordon boundary models

Boundary potential parametrization effective at the free-fermion point

Abstract

The sinh-Gordon model with integrable boundary conditions is considered in low order perturbation theory. It is pointed out that results obtained by Ghoshal for the sine-Gordon breather reflection factors suggest an interesting dual relationship between models with different boundary conditions. Ghoshal's formula for the lightest breather is checked perturbatively to $O(\beta^2)$ in the special set of cases in which the $\phi\to -\phi$ symmetry is maintained. It is noted that the parametrisation of the boundary potential which is natural for the semi-classical approximation also provides a good parametrisation at the `free-fermion' point.