Hypergravity in AdS_3

TL;DR

This paper demonstrates that a previously flat-space model for massless higher-spin fields in three dimensions can be extended to anti-de Sitter space by including a massless spin-4 field, forming a supergroup-based Chern-Simons theory.

Contribution

It introduces a deformation of the Aragone-Deser model into AdS space by adding a spin-4 field, leading to a supergroup Chern-Simons formulation with generalizations to higher spins.

Findings

Deformation into AdS space is possible with a spin-4 field.

The resulting theory is a Chern-Simons model based on OSp(1,4).

Generalization to OSp(1,2n) includes multiple bosonic and fermionic fields.

Abstract

Thirty years ago Aragone and Deser showed that in three dimensions there exists a consistent model describing interaction for massless spin-2 and spin-5/2 fields. It was crucial that these fields lived in a flat Minkowski space and as a result it was not possible to deform such model into anti-de Sitter space. In this short note we show that such deformation becomes possible provided one compliment to the model with massless spin-4 field. Resulting theory can be considered as a Chern-Simons one with a well-known supergroup OSp(1,4). Moreover there exists straightforward generalization to the OSp(1,2n) case containing a number of bosonic fields with even spins 2,4,...,2n and one fermionic field with spin n+1/2.