Supersymmetric Models on AdS3 and AdS4 Embedding Superspaces

TL;DR

This paper develops supersymmetric models on AdS3 and AdS4 spaces using superspace techniques, revealing differences in supersymmetry transformations and mass relations compared to flat space models.

Contribution

It introduces a superspace formulation of supersymmetric models on AdS3 and AdS4, highlighting novel features of supersymmetry transformations in curved backgrounds.

Findings

Supersymmetry on AdS3 is the 'square root' of AdS3 isometry transformations.

Mass relations differ from flat space due to non-isometry momentum.

A model in AdS4 relates bosonic and fermionic fields through a new symmetry transformation.

Abstract

Superspace techniques are used to formulate a supersymmetric model on an AdS3 surface embedded in four dimensions. In this model, the supersymmetry transformation is the "square root" of the transformation generated by the isometry generators of AdS3. Since 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 AdS3 space. In one coordinate system, it is possible to define a subspace with a Minkowski metric. It becomes possible to infer a model in AdS4 space in which there is a symmetry transformation that relates Bosonic and Fermionic fields. This model is not a consequence of being formulated in superspace and the Fermionic transformation is not the "square root" of an isometry of AdS4.