N=1 Supersymmetric Boundary Bootstrap

TL;DR

This paper develops a method for determining exact reflection matrices in N=1 supersymmetric boundary quantum field theories, extending the boundary bootstrap approach to include supersymmetric indices and applying it to several integrable models.

Contribution

It introduces rules for calculating supersymmetric reflection factors and boundary bound states in integrable models with N=1 boundary supersymmetry, building on known non-supersymmetric solutions.

Findings

Derived reflection matrices for boundary sine-Gordon and affine Toda models.

Established rules for supersymmetric boundary bound state spectra.

Applied the framework to free particles and sinh-Gordon models.

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_1S_0, R=R_1R_0, where S_0 and R_0 are the S-matrix and reflection matrix of some integrable non-supersymmetric boundary theory that is assumed to be known, and S_1 and R_1 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.