Hypergravity in five dimensions

TL;DR

This paper develops a consistent five-dimensional hypergravity theory involving a spin-5/2 field, extended gauge symmetries, and a Chern-Simons formulation, expanding the understanding of higher-spin gravities.

Contribution

It introduces a novel five-dimensional hypergravity model with a unique gauge algebra and a Chern-Simons action, including new fields and symmetries not previously explored.

Findings

Consistent coupling of spin-5/2 field to gravity in 5D.

Formulation of hypergravity as a Chern-Simons gauge theory.

Extension of hyper-Poincaré algebra with new generators.

Abstract

We show that a spin-$5/2$ field can be consistently coupled to gravitation without cosmological constant in five-dimensional spacetimes. The fermionic gauge "hypersymmetry" requires the presence of a finite number of additional fields, including a couple of $U(1)$ fields, a spinorial two-form, the dual of the graviton (of mixed $(2,1)$ Young symmetry) and a spin-$3$ field. The gravitational sector of the action is described by the purely quadratic Gauss-Bonnet term, so that the field equations for the metric are of second order. The local gauge symmetries of the full action principle close without the need of auxiliary fields. The field content corresponds to the components of a connection for an extension of the "hyper-Poincar\'e" algebra, which apart from the Poincar\'e and spin-$3/2$ generators, includes a generator of spin $2$ and a $U(1)$ central extension. It is also shown that this algebra admits an invariant trilinear form, which allows to formulate hypergravity as a gauge theory described by a Chern-Simons action in five dimensions.