Skip to main content
SpringerLink
Log in

Hidden conformal symmetry of extremal Kaluza-Klein black hole in four dimensions

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study the hidden conformal symmetry of four-dimensional extremal Kaluza-Klein black hole. The scalar Laplacian corresponding to the radial equation in the near-region is rewritten in terms of the \( {\text{SL}}\left( {2,\mathbb{R}} \right) \) quadratic Casimir. Using the first law of black hole thermodynamics, this symmetry enables us to obtain the conjugate charges for the CFT side. The real-time correlators are also found to agree with the CFT expectations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  2. J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. J. de Boer, M.M. Sheikh-Jabbari and J. Simon, Near Horizon Limits of Massless BTZ and Their CFT Duals, arXiv:1011.1897 [SPIRES].

  4. V. Balasubramanian, J. Parsons and S.F. Ross, States of a chiral 2d CFT, Class. Quant. Grav. 28 (2011) 045004 [arXiv:1011.1803] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. Y. Matsuo and T. Nishioka, New Near Horizon Limit in Kerr/CFT, JHEP 12 (2010) 073 [arXiv:1010.4549] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  6. T. Azeyanagi, N. Ogawa and S. Terashima, Emergent AdS 3 in the Zero Entropy Extremal Black Holes, arXiv:1010.4291 [SPIRES].

  7. J. Gegenberg, H. Liu, S.S. Seahra and B.K. Tippett, A Tomimatsu-Sato/CFT correspondence, arXiv:1010.2803 [SPIRES].

  8. M. Guica and A. Strominger, Microscopic Realization of the Kerr/CFT Correspondence, JHEP 02 (2011) 010 [arXiv:1009.5039] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Galajinsky, Particle dynamics near extreme Kerr throat and supersymmetry, JHEP 11 (2010) 126 [arXiv:1009.2341] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. B.K. Button, L. Rodriguez and C.A. Whiting, A Near Horizon CFT Dual for Kerr-Newman-AdS, arXiv:1009.1661 [SPIRES].

  11. S. Detournay, D. Israel, J.M. Lapan and M. Romo, String Theory on Warped AdS 3 and Virasoro Resonances, JHEP 01 (2011) 030 [arXiv:1007.2781] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. A.P. Porfyriadis and F. Wilczek, Effective Action, Boundary Conditions and Virasoro Algebra for AdS 3, arXiv:1007.1031 [SPIRES].

  13. B.C. da Cunha and A.R. de Queiroz, Kerr-CFT From Black-Hole Thermodynamics, JHEP 08 (2010) 076 [arXiv:1006.0510] [SPIRES].

    Article  ADS  Google Scholar 

  14. A. Castro, A. Maloney and A. Strominger, Hidden Conformal Symmetry of the Kerr Black Hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. C. Krishnan, Hidden Conformal Symmetries of Five-Dimensional Black Holes, JHEP 07 (2010) 039 [arXiv:1004.3537] [SPIRES].

    Article  ADS  Google Scholar 

  16. C.-M. Chen and J.-R. Sun, Hidden Conformal Symmetry of the Reissner-Nordström Black Holes, JHEP 08 (2010) 034 [arXiv:1004.3963] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. Y.-Q. Wang and Y.-X. Liu, Hidden Conformal Symmetry of the Kerr-Newman Black Hole, JHEP 08 (2010) 087 [arXiv:1004.4661] [SPIRES].

    Article  ADS  Google Scholar 

  18. B. Chen and J. Long, Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence, JHEP 06 (2010) 018 [arXiv:1004.5039] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. R. Li, M.-F. Li and J.-R. Ren, Entropy of Kaluza-Klein Black Hole from Kerr/CFT Correspondence, Phys. Lett. B 691 (2010) 249 [arXiv:1004.5335] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. D. Chen, P. Wang and H. Wu, Hidden conformal symmetry of rotating charged black holes, Gen. Rel. Grav. 43 (2011) 181 [arXiv:1005.1404] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. M. Becker, S. Cremonini and W. Schulgin, Correlation Functions and Hidden Conformal Symmetry of Kerr Black Holes, JHEP 09 (2010) 022 [arXiv:1005.3571] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. B. Chen and J. Long, On Holographic description of the Kerr-Newman-AdS-dS black holes, JHEP 08 (2010) 065 [arXiv:1006.0157] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. H. Wang, D. Chen, B. Mu and H. Wu, Hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-Dilaton-Axion black holes, JHEP 11 (2010) 002 [arXiv:1006.0439] [SPIRES].

    Google Scholar 

  24. R. Fareghbal, Hidden Conformal Symmetry of Warped AdS 3 Black Holes, Phys. Lett. B 694 (2010) 138 [arXiv:1006.4034] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  25. C.-M. Chen, Y.-M. Huang, J.-R. Sun, M.-F. Wu and S.-J. Zou, On Holographic Dual of the Dyonic Reissner-Nordström Black Hole, Phys. Rev. D 82 (2010) 066003 [arXiv:1006.4092] [SPIRES].

    ADS  Google Scholar 

  26. C.-M. Chen, Y.-M. Huang, J.-R. Sun, M.-F. Wu and S.-J. Zou, Twofold Hidden Conformal Symmetries of the Kerr-Newman Black Hole, Phys. Rev. D 82 (2010) 066004 [arXiv:1006.4097] [SPIRES].

    ADS  Google Scholar 

  27. R. Li, M.-F. Li and J.-R. Ren, Hidden Conformal Symmetry of Self-Dual Warped AdS 3 Black Holes in Topological Massive Gravity, arXiv:1007.1357 [SPIRES].

  28. Y. Matsuo, T. Tsukioka and C.-M. Yoo, Notes on the Hidden Conformal Symmetry in the Near Horizon Geometry of the Kerr Black Hole, Nucl. Phys. B 844 (2011) 146 [arXiv:1007.3634] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. B. Chen, J. Long and J.-j. Zhang, Hidden Conformal Symmetry of Extremal Black Holes, Phys. Rev. D 82 (2010) 104017 [arXiv:1007.4269] [SPIRES].

    ADS  Google Scholar 

  30. K.-N. Shao and Z. Zhang, Hidden Conformal Symmetry of Rotating Black Hole with four Charges, arXiv:1008.0585 [SPIRES].

  31. M.R. Setare and V. Kamali, Hidden Conformal Symmetry of Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity, Phys. Rev. D 82 (2010) 086005 [arXiv:1008.1123] [SPIRES].

    ADS  Google Scholar 

  32. A.M. Ghezelbash, V. Kamali and M.R. Setare, Hidden Conformal Symmetry of Kerr-Bolt Spacetimes, Phys. Rev. D 82 (2010) 124051 [arXiv:1008.2189] [SPIRES].

    ADS  Google Scholar 

  33. B. Chen and J. Long, Hidden Conformal Symmetry and Quasi-normal Modes, Phys. Rev. D 82 (2010) 126013 [arXiv:1009.1010] [SPIRES].

    ADS  Google Scholar 

  34. B. Chen, A.M. Ghezelbash, V. Kamali and M.R. Setare, Holographic description of Kerr-Bolt-AdS-dS Spacetimes, arXiv:1009.1497 [SPIRES].

  35. R. Li and J.-R. Ren, Holographic Dual of Linear Dilaton Black Hole in Einstein-Maxwell-Dilaton-A xion Gravity, JHEP 09 (2010) 039 [arXiv:1009.3139] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. B. Chen, C.-M. Chen and B. Ning, Holographic Q-picture of Kerr-Newman-AdS-dS Black Hole, arXiv:1010.1379 [SPIRES].

  37. M.R. Setare and V. Kamali, Hidden Conformal Symmetry of Extremal Kerr-Bolt Spacetimes, JHEP 10 (2010) 074 [arXiv:1011.0809] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. C.M. Chen, V. Kamali and M.R. Setare, Holographic Q-Picture of Black Holes in Five Dimensional Minimal Supergravity, arXiv:1011.4556 [SPIRES].

  39. B. Chen and J.-j. Zhang, Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry, arXiv:1012.2219 [SPIRES].

  40. B. Chen and C.-S. Chu, Real-time correlators in Kerr/CFT correspondence, JHEP 05 (2010) 004 [arXiv:1001.3208] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. J.M. Maldacena and A. Strominger, Universal low-energy dynamics for rotating black holes, Phys. Rev. D 56 (1997) 4975 [hep-th/9702015] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  42. D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. D. Rasheed, The Rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [SPIRES].

    Article  ADS  Google Scholar 

  45. T. Azeyanagi, N. Ogawa and S. Terashima, Holographic Duals of Kaluza-Klein Black Holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. G.W. Gibbons and D.L. Wiltshire, Black Holes in Kaluza-Klein Theory, Ann. Phys. 167 (1986) 201 [Erratum ibid. 176 (1987) 393] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. V.P. Frolov, A.I. Zelnikov and U. Bleyer, Charged Rotating Black Hole From Five-Dimensional Point Of View, Ann. Phys. 44 (1987) 371.

    Article  MathSciNet  Google Scholar 

  48. J.-i. Koga and K.-i. Maeda, Evaporation and fate of dilatonic black holes, Phys. Rev. D 52 (1995) 7066 [hep-th/9508029] [SPIRES].

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Beijing University of Technology, Beijing, 100124, China

    Yong-Chang Huang & Fang-Fang Yuan

Authors
  1. Yong-Chang Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fang-Fang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fang-Fang Yuan.

Additional information

ArXiv ePrint: 1012.5453

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, YC., Yuan, FF. Hidden conformal symmetry of extremal Kaluza-Klein black hole in four dimensions. J. High Energ. Phys. 2011, 29 (2011). https://doi.org/10.1007/JHEP03(2011)029

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP03(2011)029

Keywords

Search

Navigation