On Duality and Reflection Factors for the Sinh-gordon Model with a Boundary

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(β 2) in the special set of cases in which the φ → −φ 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.