### Abstract

We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N = 2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitrary off-shell supergravity-matter couplings. Fourthly, all maximally supersymmetric Lorentzian spaces correspond to those off-shell supergravity backgrounds for which the Grassmann-odd components of the superspace torsion and curvature tensors vanish, while the Grassmann-even components of these tensors are annihilated by the spinor derivatives.

Original language | English |
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Title of host publication | Proceedings of the Corfu Summer Institute 2014 |

Publisher | Proceedings of Science |

Number of pages | 21 |

DOIs | |

Publication status | Published - Aug 2015 |

### Publication series

Name | Proceedings of Science |
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Publisher | Sissa Medialab Srl |

ISSN (Print) | 1824-8039 |

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## Cite this

Kuzenko, S. M. (2015). Supersymmetric Spacetimes from Curved Superspace. In

*Proceedings of the Corfu Summer Institute 2014*[140] (Proceedings of Science). Proceedings of Science. https://doi.org/10.22323/1.231.0140