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The RN/CFT correspondence revisited

  • Chiang-Mei Chen
  • Jia-Rui Sun
  • Shou-Jyun Zou
Article

Abstract

We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstrøm black hole in the viewpoint of the AdS2/CFT1 correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is 6Q 2 which is different from the previous result 6Q 3 of left moving sector obtained by warped AdS3/CFT2 description. We discussed the discrepancy in these two approaches and examined novel properties of our result.

Keywords

AdS-CFT Correspondence Black Holes 2D Gravity 

References

  1. [1]
    G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [SPIRES].
  2. [2]
    L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  3. [3]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].MATHMathSciNetADSGoogle Scholar
  4. [4]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].MathSciNetADSGoogle Scholar
  5. [5]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].MATHMathSciNetGoogle Scholar
  6. [6]
    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].MATHCrossRefMathSciNetADSGoogle Scholar
  7. [7]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].Google Scholar
  8. [8]
    K. Hotta, Y. Hyakutake, T. Kubota, T. Nishinaka and H. Tanida, The CFT-interpolating black hole in three dimensions, JHEP 01 (2009) 010 [arXiv:0811.0910] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  9. [9]
    H. Lü, J. Mei and C.N. Pope, Kerr/CFT correspondence in diverse dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [SPIRES].CrossRefGoogle Scholar
  10. [10]
    T. Azeyanagi, N. Ogawa and S. Terashima, Holographic duals of Kaluza-Klein black holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    D.D.K. Chow, M. Cvetič, H. Lü and C.N. Pope, Extremal black hole/CFT correspondence in (gauged) supergravities, Phys. Rev. D 79 (2009) 084018 [arXiv:0812.2918] [SPIRES].ADSGoogle Scholar
  12. [12]
    T. Azeyanagi, N. Ogawa and S. Terashima, The Kerr/CFT correspondence and string theory, Phys. Rev. D 79 (2009) 106009 [arXiv:0812.4883] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    Y. Nakayama, Emerging AdS from extremally rotating NS5-branes, Phys. Lett. B 673 (2009) 272 [arXiv:0812.2234] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    H. Isono, T.-S. Tai and W.-Y. Wen, Kerr/CFT correspondence and five-dimensional BMPV black holes, arXiv:0812.4440 [SPIRES].
  15. [15]
    J.-J. Peng and S.-Q. Wu, Extremal Kerr black hole/CFT correspondence in the five dimensional Gödel universe, Phys. Lett. B 673 (2009) 216 [arXiv:0901.0311] [SPIRES].MathSciNetADSGoogle Scholar
  16. [16]
    C.-M. Chen and J.E. Wang, Holographic duals of black holes in five-dimensional minimal supergravity, arXiv:0901.0538 [SPIRES].
  17. [17]
    F. Loran and H. Soltanpanahi, 5D extremal rotating black holes and CFT duals, Class. Quant. Grav. 26 (2009) 155019 [arXiv:0901.1595] [SPIRES].CrossRefADSGoogle Scholar
  18. [18]
    A.M. Ghezelbash, Kerr/CFT correspondence in the low energy limit of heterotic string theory, JHEP 08 (2009) 045 [arXiv:0901.1670] [SPIRES].CrossRefADSGoogle Scholar
  19. [19]
    H. Lü, J.-w. Mei, C.N. Pope and J.F. Vazquez-Poritz, Extremal static AdS black hole/CFT correspondence in gauged supergravities, Phys. Lett. B 673 (2009) 77 [arXiv:0901.1677] [SPIRES].ADSGoogle Scholar
  20. [20]
    A.J. Amsel, G.T. Horowitz, D. Marolf and M.M. Roberts, No dynamics in the extremal Kerr throat, JHEP 09 (2009) 044 [arXiv:0906.2376] [SPIRES].CrossRefGoogle Scholar
  21. [21]
    O.J.C. Dias, H.S. Reall and J.E. Santos, Kerr-CFT and gravitational perturbations, JHEP 08 (2009) 101 [arXiv:0906.2380] [SPIRES].CrossRefGoogle Scholar
  22. [22]
    G. Compere, K. Murata and T. Nishioka, Central charges in extreme black hole/CFT correspondence, JHEP 05 (2009) 077 [arXiv:0902.1001] [SPIRES].CrossRefADSGoogle Scholar
  23. [23]
    C. Krishnan and S. Kuperstein, A comment on Kerr-CFT and Wald entropy, Phys. Lett. B 677 (2009) 326 [arXiv:0903.2169] [SPIRES].MathSciNetADSGoogle Scholar
  24. [24]
    K. Hotta, Holographic RG flow dual to attractor flow in extremal black holes, Phys. Rev. D 79 (2009) 104018 [arXiv:0902.3529] [SPIRES].ADSGoogle Scholar
  25. [25]
    D. Astefanesei and Y.K. Srivastava, CFT duals for attractor horizons, Nucl. Phys. B 822 (2009) 283 [arXiv:0902.4033] [SPIRES].CrossRefGoogle Scholar
  26. [26]
    W.-Y. Wen, Holographic descriptions of (near-)extremal black holes in five dimensional minimal supergravity, arXiv:0903.4030 [SPIRES].
  27. [27]
    T. Azeyanagi, G. Compere, N. Ogawa, Y. Tachikawa and S. Terashima, Higher-derivative corrections to the asymptotic Virasoro symmetry of 4D extremal black holes, Prog. Theor. Phys. 122 (2009) 355 [arXiv:0903.4176] [SPIRES].MATHCrossRefADSGoogle Scholar
  28. [28]
    X.-N. Wu and Y. Tian, Extremal isolated horizon/CFT correspondence, Phys. Rev. D 80 (2009) 024014 [arXiv:0904.1554] [SPIRES].ADSGoogle Scholar
  29. [29]
    Y. Matsuo, T. Tsukioka and C.-M. Yoo, Another realization of Kerr/CFT correspondence, Nucl. Phys. B 825 (2010) 231 [arXiv:0907.0303] [SPIRES].CrossRefGoogle Scholar
  30. [30]
    I. Bredberg, T. Hartman, W. Song and A. Strominger, Black hole superradiance from Kerr/CFT, arXiv:0907.3477 [SPIRES].
  31. [31]
    M. Cvetič and F. Larsen, Greybody factors and charges in Kerr/CFT, JHEP 09 (2009) 088 [arXiv:0908.1136] [SPIRES].CrossRefGoogle Scholar
  32. [32]
    T. Hartman, W. Song and A. Strominger, Holographic derivation of Kerr-Newman scattering amplitudes for general charge and spin, arXiv:0908.3909 [SPIRES].
  33. [33]
    V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2D CFT? And what does it have to do with extremal black holes?, arXiv:0906.3272 [SPIRES].
  34. [34]
    A.J. Amsel, D. Marolf and M.M. Roberts, On the stress tensor of Kerr/CFT, JHEP 10 (2009) 021 [arXiv:0907.5023] [SPIRES].CrossRefGoogle Scholar
  35. [35]
    A. Castro and F. Larsen, Near extremal Kerr entropy from AdS 2 quantum gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [SPIRES].CrossRefGoogle Scholar
  36. [36]
    T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT duals for extreme black holes, JHEP 04 (2009) 019 [arXiv:0811.4393] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  37. [37]
    M.R. Garousi and A. Ghodsi, The RN/CFT correspondence, arXiv:0902.4387 [SPIRES].
  38. [38]
    V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  39. [39]
    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [SPIRES].MATHCrossRefADSGoogle Scholar
  40. [40]
    B. Bertotti, Uniform electromagnetic field in the theory of general relativity, Phys. Rev. 116 (1959) 1331 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  41. [41]
    I. Robinson, A solution of the Maxwell-Einstein equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7 (1959) 351 [SPIRES].MATHGoogle Scholar
  42. [42]
    J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  43. [43]
    T. Hartman and A. Strominger, Central charge for AdS 2 quantum gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  44. [44]
    A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic description of AdS 2 black holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  45. [45]
    M. Alishahiha and F. Ardalan, Central charge for 2D gravity on AdS 2 and AdS 2 /CFT 1 correspondence, JHEP 08 (2008) 079 [arXiv:0805.1861] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  46. [46]
    A. Sen, Entropy function and AdS 2 /CFT 1 correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [SPIRES].CrossRefADSGoogle Scholar
  47. [47]
    R.K. Gupta and A. Sen, AdS 3 /CFT 2 to AdS 2 /CFT 1, JHEP 04 (2009) 034 [arXiv:0806.0053] [SPIRES].CrossRefMathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Department of Physics and Center for Mathematics and Theoretical PhysicsNational Central UniversityChungliTaiwan
  2. 2.Department of PhysicsNational Central UniversityChungliTaiwan

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