Abstract
We use equivariant localization to construct off-shell entropy functions for supersymmetric black holes in \(\mathcal{N}\) = 2, D = 4 gauged supergravity coupled to matter. This allows one to compute the black hole entropy without solving the supergravity equations of motion and provides a novel generalization of the attractor mechanism. We consider magnetically charged black holes in AdS4 which have an AdS2 × M2 near horizon geometry, where M2 is a sphere or a spindle, and we also obtain entropy functions for ungauged supergravity as a simple corollary. We derive analogous results for black strings and rings in D = 5 supergravity which have an AdS3 × M2 near horizon geometry, and in this setting we derive an off-shell expression for the central charge of the dual \(\mathcal{N}\) = (0, 2), d = 2 SCFT.
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Acknowledgments
We thank Seyed Morteza Hosseini, David Katona, Gabriel Lopes Cardoso, James Lucietti and Minwoo Suhfor helpful discussions. This work was supported in part by STFC grants ST/T000791/1 and ST/T000864/1, and EPSRC grant EP/R014604/1. JPG is supported as a Visiting Fellow at the Perimeter Institute. PBG is supported by the SNSF Ambizione grant PZ00P2_208666. AL is supported by the Palmer scholarship in Mathematical Physics of Merton college. JPG and JFS would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Black holes: bridges between number theory and holographic quantum information” where work on this paper was undertaken.
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Genolini, P.B., Gauntlett, J.P., Jiao, Y. et al. Localization and attraction. J. High Energ. Phys. 2024, 152 (2024). https://doi.org/10.1007/JHEP05(2024)152
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DOI: https://doi.org/10.1007/JHEP05(2024)152