# Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes

## TL;DR

This paper explores how ultra-spinning black holes in holography relate to conformal quantum mechanics, revealing a connection through holomorphic factorisation and simplifying the superconformal index in certain limits.

## Contribution

It establishes a link between ultra-spinning black holes and conformal quantum mechanics, showing how the superconformal index reduces to a single block in the limit.

## Key findings

- Ultra-spinning black holes correspond to ensembles in conformal quantum mechanics.
- The superconformal index simplifies to a single block in the ultra-spinning limit.
- The limit reveals a holomorphic factorisation structure in the dual theories.

## 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.