New Gauge Supergravity in Seven and Eleven Dimensions

Ricardo Troncoso; Jorge Zanelli

doi:10.1103/PhysRevD.58.101703

paper

New Gauge Supergravity in Seven and Eleven Dimensions

arXiv:hep-th/9710180 · doi:10.1103/PhysRevD.58.101703

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 $s p (2)$ gauge connection ( $a_{μ j}^{i}$ ). These fields form a connection for $os p (2∣8)$ . 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, $b_{μ}^{ab c d e}$ . These fields form a connection for $os p (32∣1)$ . 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.

5pages, RevTeX, no figures, two columns, minor typos corrected

New Gauge Supergravity in Seven and Eleven Dimensions

Abstract

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