The Uniqueness of Hypergravity

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.