Boundary S matrices with N=2 supersymmetry

We propose the exact boundary S matrix for breathers of the N=2 supersymmetric sine-Gordon model. We argue that this S matrix has three independent parameters, in agreement with a recently-proposed action. We also show, contrary to a previous claim, that the “universal” supersymmetric boundary S matrix commutes with two supersymmetry charges. General N=2 supersymmetric boundary integrable models are expected to have boundary S matrices with a similar structure.