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arXiv · 2210.17088

Superspace approaches to $\mathcal{N}=1$ supergravity

S. M. Kuzenko·E. S. N. Raptakis·G. Tartaglino-Mazzucchelli
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Abstract

The superspace formalism for $\mathcal{N}=1$ supergravity in four dimensions is a powerful geometric setting to engineer off-shell supergravity-matter theories, including higher-derivative couplings. This review provides a unified description of the three superspace approaches to $\mathcal{N}=1$ conformal supergravity: (i) conformal superspace; (ii) $\mathsf{U}(1)$ superspace; and (iii) the Grimm-Wess-Zumino formalism. The prepotential formulation for the latter is discussed. We briefly describe the known off-shell formulations for Poincar\'e and anti-de Sitter supergravity theories as conformal supergravity coupled to certain compensators. As simple applications of the formalism, we present the superfield equations of motion for various off-shell formulations for pure Poincar\'e and anti-de Sitter supergravity, and show that every solution of these equations is also a solution of the equations of motion for conformal supergravity.

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S. M. Kuzenko, E. S. N. Raptakis, G. Tartaglino-Mazzucchelli. 2022-10-31. Superspace approaches to $\mathcal{N}=1$ supergravity. https://arxiv.org/abs/2210.17088

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