New Gauge Supergravity in Seven and Eleven Dimensions

TL;DR

This paper introduces new supergravity theories in seven and eleven dimensions based on Chern-Simons forms, featuring off-shell supersymmetry closure and connections to extended superalgebras.

Contribution

It constructs novel gauge supergravity models in D=7 and D=11 using Chern-Simons forms, with off-shell supersymmetry and explicit algebraic structures.

Findings

The D=7 theory is an N=2 supergravity with osp(2|8) symmetry.

The D=11 theory is an N=1 supergravity with osp(32|1) symmetry.

Both theories have nonnegative energy around AdS backgrounds.

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 ($e_{\mu}^{a}$), 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.