Higher dimensional Chern-Simons supergravity

TL;DR

This paper introduces a higher-dimensional Chern-Simons supergravity theory applicable in all odd dimensions, featuring a supersymmetric extension of the Poincaré group with off-shell supersymmetry closure.

Contribution

It proposes a novel Chern-Simons supergravity action for all odd dimensions with a supersymmetric extension of the Poincaré group that closes off shell without auxiliary fields.

Findings

In 2+1 dimensions, the gauge group reduces to super-Poincaré.

In 5 dimensions, the gauge group includes a central charge.

The supersymmetry algebra closes off shell without auxiliary fields.

Abstract

A Chern-Simons action for supergravity in odd-dimensional spacetimes is proposed. For all odd dimensions, the local symmetry group is a non trivial supersymmetric extension of the Poincar\'e group. In $2+1$ dimensions the gauge group reduces to super-Poincar\'e, while for $D=5$ it is super-Poincar\'e with a central charge. In general, the extension is obtained by the addition of a 1-form field which transforms as an antisymmetric fifth-rank tensor under Lorentz rotations. Since the Lagrangian is a Chern-Simons density for the supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields.