Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT

TL;DR

This paper extends hidden conformal symmetry concepts to higher-dimensional Kerr-(A)dS black holes using Killing towers, establishing a direct link between symmetries and Killing tensors, and explores implications for Large-D/CFT correspondence.

Contribution

It introduces a novel tensor equation connecting SL(2,R) Casimir with the radial Klein-Gordon operator using Killing towers, generalizing hidden conformal symmetries to arbitrary dimensions.

Findings

Recovered known results for 4D and 5D black holes using monodromy methods.

Derived explicit symmetry generators for Kerr-(A)dS black holes.

Extended analysis to large-dimensional Schwarzschild black holes for Large-D/CFT.

Abstract

We generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. We build the SL(2, R) generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. Our construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: we use the Killing tower to build a novel tensor equation connecting the SL(2,R) Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions we recover previously known results that were obtained using the "near-region" limit and the monodromy method. We then perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators. We also extend this analysis to the large-dimensional Schwarzschild black hole as a step towards buliding a Large-D/CFT correspondence.