New Gauge Supergravity in Seven and Eleven Dimensions

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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 (eμᵃ), the spin connection (ωμab), two gravitini (ψμⁱ) and an sp(2) gauge connection (aμⱼⁱ). These fields form a connection for osp(2|8). In eleven dimensions the theory is an N=1 supergravity containing, apart from eμᵃ and ωμab, one gravitino ψμ, and a totally antisymmetric fifth rank Lorentz tensor one-form, bμabcde. These fields form a connection for 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]-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.