AdS (super)projectors in three dimensions and partial masslessness

Abstract

We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS${}_3$. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group $\mathsf{SO}(2,2)$ of AdS${}_3$. Their poles are demonstrated to correspond to (partially) massless fields. As an application, we make use of the projectors to recast the conformal and topologically massive higher-spin actions in AdS${}_3$ into a manifestly gauge-invariant and factorised form. We also propose operators which isolate the component of a field that is transverse and carries a definite helicity. Such fields correspond to an irreducible representation of $\mathsf{SO}(2,2)$. Our results are then extended to the case of $\mathcal{N}=1$ AdS${}_3$ supersymmetry.

arXiv comment37 pages; V2: New material added to conclusion, published version

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