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

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.