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arXiv · 2107.12201

AdS (super)projectors in three dimensions and partial masslessness

Daniel Hutchings·Sergei M. Kuzenko·Michael Ponds
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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.

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Daniel Hutchings, Sergei M. Kuzenko, Michael Ponds. 2021-10-20. AdS (super)projectors in three dimensions and partial masslessness. https://doi.org/10.1007/jhep10(2021)090

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