New gauge supergravity in seven and eleven dimensions (original) (raw)

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 (e a µ ), the spin connection (ω ab µ ), two gravitini (ψ i µ ) and an sp(2) gauge connection (a i µj ). These fields form a connection for osp(2|8). In eleven dimensions the theory is an N = 1 supergravity containing, apart from e a µ and ω ab µ , one gravitino ψµ, and a totally antisymmetric fifth rank Lorentz tensor oneform, b abcde µ . 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.