N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

TL;DR

This paper explores N=2 boundary supersymmetry in integrable models, deriving new boundary reflection matrices, studying boundary superalgebra, and providing exact results for quantum impurity problems.

Contribution

It introduces a new boundary reflection matrix and studies N=2 boundary superalgebra in integrable models, extending the understanding of boundary supersymmetry.

Findings

Derived a new boundary reflection matrix for N=2 models

Studied N=2 boundary superalgebra structure

Obtained exact results for quantum impurity models

Abstract

Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N=2 supersymmetry. A new boundary reflection matrix is obtained for this model and N=2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N=2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee-Yang model, a massive deformation of the anisotropic Kondo model at the filling values g=2/(2n+3) and the boundary Ashkin-Teller model.