Supersymmetric extension of the sine-Gordon theory with integrable boundary interactions

TL;DR

This paper investigates the supersymmetric extension of the sine-Gordon theory on a half-line, deriving boundary potentials that preserve both integrability and supersymmetry, revealing strong restrictions on boundary parameters.

Contribution

It derives boundary potentials that maintain integrability and supersymmetry in the supersymmetric sine-Gordon theory, showing these symmetries impose strict constraints.

Findings

Boundary potential preserving integrability and supersymmetry is derived.

Unlike the bosonic case, no free parameters are allowed in the boundary term.

Integrability and supersymmetry strongly restrict boundary interactions.

Abstract

Integrability and supersymmetry of the supersymmetric extension of the sine-Gordon theory on a half-line are examined and the boundary potential which preserves both the integrability and supersymmetry on the bulk is derived. It appears that unlike the boundary bosonic sine-Gordon theory, integrability and supersymmetry strongly restrict the form and parameters of the boundary potential, so that no free parameter in the boundary term is allowed up to a choice of signs.