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. ln seven dimensions the theory is an N = 2 supergravity whose fields are the vielbein (e(mu)(a)), the spin connection (omega(mu)(ab)), two gravitini (psi(mu)(l)) and an sp(2) gauge connection (a(mu j)(i)). These fields form a connection for o sp(2\8). In eleven dimensions the theory is an N = 1 supergravity containing, apart from e(mu)(a) and omega(mu)(ab), one gravitino psi(mu) and a totally antisymmetric fifth rank Lorentz tensor one-form, b(mu)(abcde). These fields form a connection for o sp(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 non-negative energy around an AdS background, which is a classical solution that saturates the Bogomol'nyi bound obtained from the superarlgebn, [S0556-2821(98)50522-X].