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.

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

References in corpus (8)

• Current Exchanges and Unconstrained Higher Spins
• Quantum W-symmetry in AdS_3
• Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space
• Off-shell massive N=1 supermultiplets in three dimensions
• Three-dimensional (p,q) AdS superspaces and matter couplings
• Conformal geometry and (super)conformal higher-spin gauge theories
• Spin projection operators in (A)dS and partial masslessness
• Linearised actions for $\mathcal{N}$-extended (higher-spin) superconformal gravity