AdS (super)projectors in three dimensions and partial masslessness

We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS₃. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group SO(2, 2) of AdS₃. 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 AdS₃ 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 irreducible representations of SO(2, 2). Our results are then extended to the case of N = 1 AdS₃ supersymmetry.