New Gauge Supergravity in Seven and Eleven Dimensions

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 ($e_μ^{a}$), the spin connection ($ω_μ^{ab}$), two gravitini ($ψ_μ^{i}$) and an $sp(2)$ gauge connection ($a_{μj}^{i}$). These fields form a connection for $osp(2|8)$. In eleven dimensions the theory is an N=1 supergravity containing, apart from $e_μ^{a}$ and $ω_μ^{ab}$, one gravitino $ψ_μ$, and a totally antisymmetric fifth rank Lorentz tensor one-form, $b_μ^{abcde}$. 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.