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### Abstract

In four spacetime dimensions, all N = 1 supergravity-matter systems can be formulated in the so-called U(1) superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background U(1) superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields ℓ(α1…αm)(α⋅1…α⋅n), with m and n non-negative integers, m + n > 0, and elaborate on their significance in the following cases: (i) m = n = 1; (ii) m − 1 = n = 0; and (iii) m = n > 1. The (conformal) Killing vector superfields ℓ _{α} _{α⋅} generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields ℓ_{α} generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with m = n > 1 prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.

Original language | English |
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Article number | 133 |

Journal | Journal of High Energy Physics |

Volume | 2020 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Apr 2020 |

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## Projects

- 1 Active

## Advances in Conformal Field Theory with Extended Symmetry

Kuzenko, S., Buchbinder, E., Theisen, S. & Tseytlin, A.

1/01/20 → 31/12/22

Project: Research

## Cite this

*Journal of High Energy Physics*,

*2020*(4), [133]. https://doi.org/10.1007/JHEP04(2020)133