Higher dimensional Chern-Simons supergravity

A Chern-Simons action for supergravity in odd-dimensional spacetimes is proposed. For all odd dimensions, the local symmetry group is a nontrivial 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 one-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.