New boundary conditions for (extended) ${\mathrm{AdS}}_3$ supergravity

Abstract

In this work, we build the most general boundary conditions for $\mathcal{N}=\left(1,1\right)$ and $\mathcal{N}=\left(2,2\right)$ extended supergravity. We show that for the loosest set of boundary conditions, their asymptotic symmetry algebras are two copies of the $\mathfrak{osp}{\left(1\mid 2\right)}_k$ and $\mathfrak{osp}{\left(2\mid 2\right)}_k$ algebra, respectively. Then, we restrict the gauge fields on the boundary conditions in order to obtain supersymmetric extensions of the Brown-Henneaux and Troessaert boundary conditions. Furthermore, for $\mathcal{N}=1$ and $\mathcal{N}=2$ (extended) supergravity we show the supersymmetric extensions of Avery-Poojary-Suryanarayana boundary conditions.

arXiv commentAdded references, corrected typos

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Cited by in corpus (14)

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• Celestial Holography: Lectures on Asymptotic Symmetries
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• Finiteness of 3D higher spin gravity Landscape
• Equivalent Dual Theories for 3D N=2 Supergravity
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• Pure and Twisted Holography
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• Note on Bulk Reconstruction in AdS${}_3$/WCFT${}_2$
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Spin-3 fields in Mielke-Baekler gravity