### Abstract

The N-extended self-dual supergravity in the ultra-hyperbolic four-dimensional space-time of kleinian signature (2 + 2) is given in the N-extended harmonic superspace. We reformulate the on-shell N-extended self-dual supergravity constraints of Siegel to a "zero-curvature" representation, and solve all of them but one in terms of a single superfield prepotential, by using a covariant Frobenius gauge in the Devchand-Ogievetsky approach. An off-shell superspace action, whose equation of motion yields the remaining constraint, is found. Our manifestly Lorentz-covariant action in harmonic superspace is very similar to the non-covariant Chern-Simons-type action, which was proposed earlier by Siegel in the light-cone N = 8 superspace. Our action is also invariant under the residual superdiffeomorphisms and the residual local OSp(8|2) super-Lorentz rotations, which are left after imposing the Frobenius gauge. The infinitesimal superfield parameters of the residual symmetries are expressed in terms of independent analytic superfields.

Original language | English |
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Pages (from-to) | 597-626 |

Number of pages | 30 |

Journal | Nuclear Physics B |

Volume | 526 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 24 Aug 1998 |

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### Keywords

- Self-duality
- Supergravity
- Superspace

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*526*(1-3), 597-626. https://doi.org/10.1016/S0550-3213(98)00266-1