Exploring Three-dimensional Higher-Spin Supergravity based on sl(N |N - 1) Chern-Simons theories

Abstract

We investigate various aspects of higher-spin anti-de Sitter supergravity in three dimensions as described by Chern-Simons theory based on the finite-dimensional superalgebra sl(N |N - 1), with the particular case of N = 3 as our prime example. This class of theories serves as a natural supersymmetrization of the higher-spin gravity theory based on sl(N) Chern-Simons theories. We demonstrate explicitly that the asymptotic symmetry algebra contains the N = 2 superconformal algebra in each sector. The appropriate Killing spinor equations are derived and used to classify existing and new classical solutions. We also discuss holonomy conditions, higher-spin black holes and conical defect spacetimes in this class of theories.

41 pages, a few typos in v4 corrected

References in corpus (4)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Triality in Minimal Model Holography

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• A note on conical solutions in 3D Vasiliev theory
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• Conical defects and N=2 higher spin holography
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• Modular Properties of 3D Higher Spin Theory
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• Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $Ad{S}_3$ Supergravity
• Higher-spin gauge theories in three spacetime dimensions
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• Finiteness of 3D higher spin gravity Landscape
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• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
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• On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary
• Higher Spin Chern-Simons Theory and the Super Boussinesq hierarchy
• On scalar propagators of three-dimensional higher-spin black holes