Hidden conformal symmetries from Killing towers with an application to large-D/CFT

Keeler, Cynthia; Martin, Victoria; Priya, Alankrita

doi:10.21468/SciPostPhys.12.5.170

SciPost Physics

Hidden conformal symmetries from Killing towers with an application to large-D/CFT

Cynthia Keeler, Victoria Martin, Alankrita Priya

SciPost Phys. 12, 170 (2022) · published 23 May 2022

doi: 10.21468/SciPostPhys.12.5.170
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.5.170
TI  - Hidden conformal symmetries from Killing towers with an application to large-D/CFT
PY  - 2022/05/23
UR  - https://www.scipost.org/SciPostPhys.12.5.170
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 5
SP  - 170
A1  - Keeler, Cynthia
AU  - Martin, Victoria
AU  - Priya, Alankrita
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.12.5.170,
	title={{Hidden conformal symmetries from Killing towers with an application to large-D/CFT}},
	author={Cynthia Keeler and Victoria Martin and Alankrita Priya},
	journal={SciPost Phys.},
	volume={12},
	pages={170},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.5.170},
	url={https://scipost.org/10.21468/SciPostPhys.12.5.170},
}

Cited by 4

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¹ Cynthia Keeler,
² Victoria Martin,
¹ Alankrita Priya

Funders for the research work leading to this publication