The N=1 supersymmetric bootstrap and Lie algebas

TL;DR

This paper explores the bootstrap approach for N=1 supersymmetric integrable quantum field theories, discovering new solutions with Lie algebraic structures and analyzing their implications for specific models.

Contribution

It introduces new bootstrap solutions with Lie algebraic data for N=1 supersymmetric theories, extending known models and analyzing their S-matrices.

Findings

New bootstrap solutions with affine Lie algebra data

Identification of kink states with topological charge

Closure of S-matrices for supersymmetric O(2n) sigma and sine-Gordon models

Abstract

The bootstrap programme for finding exact S-matrices of integrable quantum field theories with N=1 supersymmetry is investigated. New solutions are found which have the same fusing data as bosonic theories related to the classical affine Lie algebras. When the states correspond to a spinor spot of the Dynkin diagram they are kinks which carry a non-zero topological charge. Using these results, the S-matrices of the supersymmetric O($2n$) sigma model and sine-Gordon model can be shown to close under the bootstrap.