Abstract
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 mathcal{N} = 1 AdS3 supersymmetry.
Highlights
A few years later Rittenberg and Sokatchev [11] made use of a similar method to construct the superprojectors in N extended Minkowski superspace M4|4N
Of particular interest are the transverse projectors which are constructed in terms of the Casimir operators of so(2, 2)
We recall that an irreducible representation of iso(2, 1) with mass ρ and helicity σn/2 may be realised on the space of totally symmetric rank-n spinor fields φα(n) satisfying the differential equations
Summary
Which satisfies the commutation relation [Da, Db] = −4S2Mab ⇐⇒ [Dαβ, Dγδ] = 4S2 εγ(αMβ)δ + εδ(αMβ)γ. Eam is the inverse vielbein, ωabc is the Lorentz connection and the parameter S is related to the scalar curvature R via R = −24S2. The Lorentz generators with vector (Mab = −Mba) and spinor (Mαβ = Mβα) indices are defined in appendix A. For an arbitrary symmetric rank-n spinor field φα(n). The structure Dα(2)Dβ(2)φβ(2)α(n−2) in (2.4) is not defined for the cases n = 0 and n = 1. It is multiplied by n(n − 1) which vanishes for these cases
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