The scaling supersymmetric Yang-Lee model with boundary

We define the scaling supersymmetric Yang-Lee model with boundary as the (1,3) perturbation of the superconformal minimal model SM(2/8) (or equivalently, the (1,5) perturbation of the conformal minimal model M(3/8)) with a certain conformal boundary condition. We propose the corresponding boundary S matrix, which is not diagonal for general values of the boundary parameter. We argue that the model has an integral of motion corresponding to an unbroken supersymmetry, and that the proposed S matrix commutes with a similar quantity. We also show by means of a boundary TBA analysis that the proposed boundary S matrix is consistent with massless flow away from the ultraviolet conformal boundary condition.