### 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 |
---|---|

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 |

### Fingerprint

### 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

**An action of n = 8 self-dual supergravity in ultra-hyperbolic harmonic superspace.** / Karnas, Siniša; Ketov, Sergei V.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 526, no. 1-3, pp. 597-626. https://doi.org/10.1016/S0550-3213(98)00266-1

}

TY - JOUR

T1 - An action of n = 8 self-dual supergravity in ultra-hyperbolic harmonic superspace

AU - Karnas, Siniša

AU - Ketov, Sergei V.

PY - 1998/8/24

Y1 - 1998/8/24

N2 - 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.

AB - 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.

KW - Self-duality

KW - Supergravity

KW - Superspace

UR - http://www.scopus.com/inward/record.url?scp=0032563544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032563544&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(98)00266-1

DO - 10.1016/S0550-3213(98)00266-1

M3 - Article

AN - SCOPUS:0032563544

VL - 526

SP - 597

EP - 626

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-3

ER -