Abstract
We study a limit in which a relativistic CFT reduces to conformal quantum mechanics, and relate the partition functions of the two theories. When the initial CFT is holographic, our limit coincides with an ultra-spinning limit in the gravity dual. We therefore propose that ultra-spinning black holes are dual to an appropriate ensemble in finite-dimensional conformal quantum mechanics. The limit is studied in detail for SCFTs in four and six dimensions. These theories have a superconformal index which can be computed by gluing together two or more blocks. Applying our limit to the index effectively isolates a single such block. Our results therefore suggest that ultra-spinning black holes play the role of blocks in the gravitational dual of holomorphic factorisation.
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Acknowledgments
We would like to thank Kimyeong Lee, Dario Martelli and Sam Crew for useful discussions. We would also like to thank Chiung Hwang for collaboration in an early stage of this project. R.M. was supported by David Tong’s Simons Investigator Award. This work has been partially supported by STFC consolidated grant ST/T000694/1.
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Dorey, N., Mouland, R. Conformal quantum mechanics, holomorphic factorisation, and ultra-spinning black holes. J. High Energ. Phys. 2024, 86 (2024). https://doi.org/10.1007/JHEP02(2024)086
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DOI: https://doi.org/10.1007/JHEP02(2024)086