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 ($e_{ \mu}^{ a}$), the spin connection ($\omega_{ \mu}^{ ab}$), two gravitini ($\psi_{ \mu}^{ i}$) and an $sp(2)$ gauge connection ($a_{ \mu j}^{ i}$). These fields form a connection for $osp(2|8)$. 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 $osp(32|1)$. 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.
Categories: hep-th