N=1 supersymmetric boundary bootstrap

Abstract

We investigate the boundary bootstrap programme for finding exact reflection matrices of integrable boundary quantum field theories with N=1 boundary supersymmetry. The bulk S-matrix and the reflection matrix are assumed to take the form S ̂ = S ̃ S , R ̂ = R ̃ R , where S̃ and R̃ are the S-matrix and reflection matrix of some integrable non-supersymmetric boundary theory that is assumed to be known, and S and R describe the mixing of supersymmetric indices. Under the assumption that the bulk particles transform in the kink and boson/fermion representations and the ground state is a singlet we present rules by which the supersymmetry representations and reflection factors for excited boundary bound states can be determined. We apply these rules to the boundary sine-Gordon model, to the boundary a 2 (1) and a 4 (1) affine Toda field theories, to the boundary sinh-Gordon model and to the free particle.