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

Cynthia Keeler; Victoria Martin; Alankrita Priya

doi:10.21468/SciPostPhys.12.5.170

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

Cynthia Keeler, Victoria Martin, Alankrita Priya

Science Institute

University of Iceland

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	170
Journal	SciPost Physics
Volume	12
Issue number	5
DOIs	https://doi.org/10.21468/SciPostPhys.12.5.170
Publication status	Published - 23 May 2022

Bibliographical note

Funding Information: We thank Alex Chanson, Fridrik Freyr Gautason, Valentina Giangreco M. Puletti, Rahul Poddar, Maria Rodriguez, Watse Sybesma and Lárus Thorlacius for illuminating conversations. The work of CK and AP is supported by the U.S. Department of Energy under grant number DESC0019470. The work of VM is supported by the Icelandic Research Fund under grant 195970-052. Publisher Copyright: © 2022 American Association for the Advancement of Science.

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10.21468/SciPostPhys.12.5.170

Cite this

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title = "Hidden conformal symmetries from Killing towers with an application to 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.",

author = "Cynthia Keeler and Victoria Martin and Alankrita Priya",

note = "Funding Information: We thank Alex Chanson, Fridrik Freyr Gautason, Valentina Giangreco M. Puletti, Rahul Poddar, Maria Rodriguez, Watse Sybesma and L{\'a}rus Thorlacius for illuminating conversations. The work of CK and AP is supported by the U.S. Department of Energy under grant number DESC0019470. The work of VM is supported by the Icelandic Research Fund under grant 195970-052. Publisher Copyright: {\textcopyright} 2022 American Association for the Advancement of Science.",

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doi = "10.21468/SciPostPhys.12.5.170",

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AU - Martin, Victoria

AU - Priya, Alankrita

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PY - 2022/5/23

Y1 - 2022/5/23

N2 - 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.

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.

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DO - 10.21468/SciPostPhys.12.5.170

M3 - Article

SN - 2542-4653

VL - 12

JO - SciPost Physics

JF - SciPost Physics

IS - 5

M1 - 170

ER -

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

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Bibliographical note

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