Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
arXiv:2302.14850 · doi:10.1007/JHEP02(2024)086
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.
arXiv comment57 pages. Minor clarifications, citations added. Matches published version
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