Superspace techniques are used to formulate a supersymmetric model on an AdS_3 surface embedded in four dimensions. In this model, the supersymmetry transformation is the "square root" of the transformation generated by the isometry generators of AdS_3. Because momentum is not an isometry generator, supersymmetry does not result in equal masses for a bosonic field and its fermionic partner. We express this model in terms of coordinates that characterize the AdS_3 space. In one coordinate system, it is possible to define a subspace with a Minkowski metric. It becomes possible to infer a model in AdS_4 space in which there is a symmetry transformation that relates bosonic and fermionic fields. This model is not a consequence of being formulated in a superspace and the fermionic symmetry transformation is not the "square root" of an isometry of AdS_4.
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