An off-shell formulation is given for the supersymmetry in singular spaces that has recently been developed in an on-shell formalism by Bergshoeff, Kallosh and Van Proeyen using an supersymmetry singlet 'coupling constant' field and a 4-form multiplier field in five-dimensional space-time. I also identify the 4D Weyl and matter multiplets induced on the boundary planes from the 5D bulk fields, and discuss in our superconformal framework how and when the bulk cosmological constant and the brane tensions of boundary planes are mutually correlated by supersymmetry requirement.
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