Abstract

Locally supersymmetric systems in odd dimensions whose Lagrangians are Chern-Simons forms for supersymmetric extensions of anti-de Sitter gravity are discussed. The construction is illustrated for D=7 and 11. In seven dimensions the theory is an N=2 supergravity whose fields are the vielbein (eaμeμa), the spin connection (ωabμωμab), two gravitini (ψiμψμi) and an sp(2)sp(2) gauge connection (aiμjaμji). These fields form a connection for osp(2|8)osp(2|8). In eleven dimensions the theory is an N=1 supergravity containing, apart from eaμeμa and ωabμωμab, one gravitino ψμψμ, and a totally antisymmetric fifth rank Lorentz tensor one-form, babcdeμbμabcde. These fields form a connection for osp(32|1)osp(32|1). The actions are by construction invariant under local supersymmetry and the algebra closes off shell without requiring auxiliary fields. The N=2[D/2]N=2[D/2]-theory can be shown to have nonnegative energy around an AdS background, which is a classical solution that saturates the Bogomolnyi bound obtained from the superalgebra.