# The Uniqueness of Hypergravity

## TL;DR

This paper demonstrates that in 3D flat space, the only consistent interactions between certain gauge fields lead to hypergravity, with local hypersymmetry being uniquely determined by the theory's constraints.

## Contribution

It proves the uniqueness of hypergravity interactions in 3D flat space using BRST-cohomological methods under specific assumptions.

## Key findings

- Hypergravity arises as the unique consistent interaction.
- Local hypersymmetry is the only consistent gauge deformation.
- Extensions with fermions or cosmological terms face obstructions.

## Abstract

We show that consistent interactions of a spin-2 and a higher-spin Majorana fermion gauge fields in 3D flat space lead uniquely to Aragone-Deser hypergravity or its generalization. Our analysis employs the BRST-cohomological techniques, and works in the metric-like formulation under the assumptions of locality, parity and Poincar\'e invariance. Local hypersymmetry shows up as the unique consistent deformation of the gauge transformations. An extension of the theory with fermion flavors does not change these features, while a cosmological deformation becomes obstructed in the absence of other degrees of freedom and/or non-locality.