Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
arXiv:2110.10723 · doi:10.21468/SciPostPhys.12.5.170
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.
39 pages; V2
References in corpus (14)
- CFT Duals for Extreme Black Holes
- General Kerr-NUT-AdS Metrics in All Dimensions
- Kerr-AdS/CFT Correspondence in Diverse Dimensions
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Cargese Lectures on the Kerr/CFT Correspondence
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- Hidden Symmetry of Vanishing Love
- Central Charges in Extreme Black Hole/CFT Correspondence
- Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities
- Complete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
- The large D black hole Membrane Paradigm at first subleading order
- Deformed conformal symmetry of Kerr-Newman-NUT-AdS black holes
- Kerr-Newman Black Hole Entropy and Soft Hair
- Central Charges for AdS Black Holes