Abstract
We study the holographic duality between higher-spin (HS) gravity in 4d and free vector models in 3d, with special attention to the role of \( \mathcal{N} \) = 2 supersymmetry (SUSY). For the type-A bosonic bulk theory, dual to spin-0 fields on the boundary, there exists a twistor-space description; this maps both single-trace boundary operators and linearized bulk fields to spacetime-independent twistor functions, whose HS-algebra products compute all boundary correlators. Here, we extend this description to the type-B bosonic theory (dual to spin-1/2 fields on the boundary), and to the supersymmetric theory containing both. A key role is played by boundary bilocals, which in type-A are dual to the Didenko-Vasiliev 1/2-BPS “black hole”. We extend this to an infinite family of linearized 1/2-BPS “black hole” solutions. Remarkably, the full supersymmetric theory (along with the SUSY generators) fits in the same space of twistor functions as the type-A theory. Instead of two sets of bosonic bulk fields, the formalism sees one set of linearized fields, but with both types of boundary data allowed.
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Acknowledgments
We thank Per Sundell, Vyacheslav E. Didenko and Mirian Tsulaia for discussions. This work is supported by the Quantum Gravity Unit of Okinawa Institute of Science and Technology Graduate University (OIST).
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Lang, J., Neiman, Y. \( \mathcal{N} \) = 2 supersymmetry in the twistor description of higher-spin holography. J. High Energ. Phys. 2024, 341 (2024). https://doi.org/10.1007/JHEP05(2024)341
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DOI: https://doi.org/10.1007/JHEP05(2024)341