AdS (super)projectors in three dimensions and partial masslessness

TL;DR

This paper develops explicit transverse projection operators for higher-spin fields in AdS3, revealing their relation to massless and partially massless states, and applies these to reformulate higher-spin actions in a gauge-invariant form, including supersymmetric extensions.

Contribution

It introduces a systematic construction of transverse projectors for arbitrary spin fields in AdS3 using Casimir operators, and applies them to simplify higher-spin actions and extend to supersymmetry.

Findings

Projectors correspond to (partially) massless fields.

Reformulation of higher-spin actions into gauge-invariant, factorized forms.

Extension of results to $ abla=1$ AdS$_3$ supersymmetry.

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.