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Journal of High Energy Physics

, 2019:79 | Cite as

The BPS limit of rotating AdS black hole thermodynamics

  • Davide CassaniEmail author
  • Lorenzo Papini
Open Access
Regular Article - Theoretical Physics
  • 42 Downloads

Abstract

We consider rotating, electrically charged, supersymmetric AdS black holes in four, five, six and seven dimensions, and provide a derivation of the respective extremization principles stating that the Bekenstein-Hawking entropy is the Legendre transform of a homogeneous function of chemical potentials, subject to a complex constraint. Extending a recently proposed BPS limit, we start from finite temperature and reach extremality following a supersymmetric trajectory in the space of complexified solutions. We show that the entropy function is the supergravity on-shell action in this limit. Chemical potentials satisfying the extremization equations also emerge from the complexified solution.

Keywords

AdS-CFT Correspondence Black Holes in String Theory Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
  2. [2]
    F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
  3. [3]
    F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS 4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].
  4. [4]
    A. Zaffaroni, Lectures on AdS black holes, holography and localization, arXiv:1902.07176 [INSPIRE].
  5. [5]
    A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS 5 black holes, arXiv:1810.11442 [INSPIRE].
  6. [6]
    S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
  7. [7]
    F. Benini and P. Milan, Black holes in 4d N = 4 super-Yang-Mills, arXiv:1812.09613 [INSPIRE].
  8. [8]
    M. Honda, Quantum black hole entropy from 4d supersymmetric Cardy formula, Phys. Rev. D 100 (2019) 026008 [arXiv:1901.08091] [INSPIRE].
  9. [9]
    A. Arabi Ardehali, Cardy-like asymptotics of the 4d N = 4 index and AdS 5 blackholes, JHEP 06 (2019) 134 [arXiv:1902.06619] [INSPIRE].
  10. [10]
    S. Choi and S. Kim, Large AdS 6 black holes from CFT 5, arXiv:1904.01164 [INSPIRE].
  11. [11]
    J. Kim, S. Kim and J. Song, A 4d N = 1 Cardy formula, arXiv:1904.03455 [INSPIRE].
  12. [12]
    A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, The asymptotic growth of states of the 4d N = 1 superconformal index, JHEP 08 (2019) 120 [arXiv:1904.05865] [INSPIRE].
  13. [13]
    A. Amariti, I. Garozzo and G. Lo Monaco, Entropy function from toric geometry, arXiv:1904.10009 [INSPIRE].
  14. [14]
    A. Sen, Entropy function and AdS 2 /CFT 1 correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [INSPIRE].
  15. [15]
    S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS 5, JHEP 07 (2017) 106 [arXiv:1705.05383] [INSPIRE].
  16. [16]
    S.M. Hosseini, K. Hristov and A. Zaffaroni, A note on the entropy of rotating BPS AdS 7 × S 4 black holes, JHEP 05 (2018) 121 [arXiv:1803.07568] [INSPIRE].
  17. [17]
    S. Choi, C. Hwang, S. Kim and J. Nahmgoong, Entropy functions of BPS black holes in AdS 4 and AdS 6, arXiv:1811.02158 [INSPIRE].
  18. [18]
    G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
  19. [19]
    J.D. Brown, E.A. Martinez and J.W. York, Jr., Complex Kerr-Newman geometry and black hole thermodynamics, Phys. Rev. Lett. 66 (1991) 2281 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    N. Halmagyi and S. Lal, On the on-shell: the action of AdS 4 black holes, JHEP 03 (2018) 146 [arXiv:1710.09580] [INSPIRE].
  21. [21]
    F. Azzurli, N. Bobev, P.M. Crichigno, V.S. Min and A. Zaffaroni, A universal counting of black hole microstates in AdS 4, JHEP 02 (2018) 054 [arXiv:1707.04257] [INSPIRE].
  22. [22]
    A. Cabo-Bizet, U. Kol, L.A. Pando Zayas, I. Papadimitriou and V. Rathee, Entropy functional and the holographic attractor mechanism, JHEP 05 (2018) 155 [arXiv:1712.01849] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    M. Suh, On-shell action and the Bekenstein-Hawking entropy of supersymmetric black holes in AdS 6, arXiv:1812.10491 [INSPIRE].
  24. [24]
    M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Rotating black holes in gauged supergravities: thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
  25. [25]
    D.D.K. Chow, Charged rotating black holes in six-dimensional gauged supergravity, Class. Quant. Grav. 27 (2010) 065004 [arXiv:0808.2728] [INSPIRE].
  26. [26]
    I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    P.J. Silva, Thermodynamics at the BPS bound for black holes in AdS, JHEP 10 (2006) 022 [hep-th/0607056] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    C. Romelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
  29. [29]
    J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
  30. [30]
    A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    O.J.C. Dias and P.J. Silva, Euclidean analysis of the entropy functional formalism, Phys. Rev. D 77 (2008) 084011 [arXiv:0704.1405] [INSPIRE].
  32. [32]
    J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
  33. [33]
    H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS 5 black holes, JHEP 04 (2006) 036 [hep-th/0601156] [INSPIRE].
  34. [34]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  35. [35]
    M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in five dimensional U(1)3 gauged N = 2 supergravity, Phys. Rev. D 70 (2004) 081502 [hep-th/0407058] [INSPIRE].
  36. [36]
    S.-Q. Wu, General nonextremal rotating charged AdS black holes in five-dimensional U(1)3 gauged supergravity: a simple construction method, Phys. Lett. B 707 (2012) 286 [arXiv:1108.4159] [INSPIRE].
  37. [37]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Five-dimensional gauged supergravity black holes with independent rotation parameters, Phys. Rev. D 72 (2005) 041901 [hep-th/0505112] [INSPIRE].
  38. [38]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Non-extremal rotating black holes in five-dimensional gauged supergravity, Phys. Lett. B 644 (2007) 192 [hep-th/0606213] [INSPIRE].
  39. [39]
    J. Mei and C.N. Pope, New rotating non-extremal black holes in D = 5 maximal gauged supergravity, Phys. Lett. B 658 (2007) 64 [arXiv:0709.0559] [INSPIRE].
  40. [40]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
  41. [41]
    G.W. Gibbons, M.J. Perry and C.N. Pope, The first law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [INSPIRE].
  42. [42]
    S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
  43. [43]
    W. Chen, H. Lü and C.N. Pope, Mass of rotating black holes in gauged supergravities, Phys. Rev. D 73 (2006) 104036 [hep-th/0510081] [INSPIRE].
  44. [44]
    B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir energy in curved space and its supersymmetric counterpart, JHEP 07 (2015) 043 [arXiv:1503.05537] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    B. Assel, D. Cassani and D. Martelli, Supersymmetric counterterms from new minimal supergravity, JHEP 11 (2014) 135 [arXiv:1410.6487] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    I. Papadimitriou, Supercurrent anomalies in 4d SCFTs, JHEP 07 (2017) 038 [arXiv:1703.04299] [INSPIRE].
  47. [47]
    O.S. An, Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization, JHEP 12 (2017) 107 [arXiv:1703.09607] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    P. Benetti Genolini, D. Cassani, D. Martelli and J. Sparks, The holographic supersymmetric Casimir energy, Phys. Rev. D 95 (2017) 021902 [arXiv:1606.02724] [INSPIRE].
  49. [49]
    P. Benetti Genolini, D. Cassani, D. Martelli and J. Sparks, Holographic renormalization and supersymmetry, JHEP 02 (2017) 132 [arXiv:1612.06761] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    C. Closset, L. Di Pietro and H. Kim, ’t Hooft anomalies and the holomorphy of supersymmetric partition functions, JHEP 08 (2019) 035 [arXiv:1905.05722] [INSPIRE].
  51. [51]
    S. Kim and K.-M. Lee, 1/16-BPS black holes and giant gravitons in the AdS 5 × S 5 space, JHEP 12 (2006) 077 [hep-th/0607085] [INSPIRE].
  52. [52]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [INSPIRE].
  53. [53]
    D.D.K. Chow and G. Compère, Dyonic AdS black holes in maximal gauged supergravity, Phys. Rev. D 89 (2014) 065003 [arXiv:1311.1204] [INSPIRE].
  54. [54]
    V.A. Kostelecky and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [INSPIRE].
  55. [55]
    M.M. Caldarelli and D. Klemm, Supersymmetry of anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].
  56. [56]
    K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS 4, JHEP 01 (2019) 199 [arXiv:1811.00292] [INSPIRE].
  57. [57]
    L.J. Romans, The F (4) gauged supergravity in six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
  58. [58]
    M. Cvetič, H. Lü and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].
  59. [59]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Non-extremal charged rotating black holes in seven-dimensional gauged supergravity, Phys. Lett. B 626 (2005) 215 [hep-th/0412094] [INSPIRE].
  60. [60]
    K. Hristov, S. Katmadas and C. Toldo, Matter-coupled supersymmetric Kerr-Newman-AdS 4 black holes, arXiv:1907.05192 [INSPIRE].
  61. [61]
    D.D.K. Chow, Equal charge black holes and seven dimensional gauged supergravity, Class. Quant. Grav. 25 (2008) 175010 [arXiv:0711.1975] [INSPIRE].
  62. [62]
    J.P. Gauntlett, D. Martelli and J. Sparks, Toric geometry and the dual of-extremization, JHEP 06 (2019) 140 [arXiv:1904.04282] [INSPIRE].
  63. [63]
    S.M. Hosseini and A. Zaffaroni, Geometry of-extremization and black holes microstates, JHEP 07 (2019) 174 [arXiv:1904.04269] [INSPIRE].
  64. [64]
    H. Kim and N. Kim, Black holes with baryonic charge and-extremization, arXiv:1904.05344 [INSPIRE].
  65. [65]
    J.L. Blázquez-Salcedo, J. Kunz, F. Navarro-Lérida and E. Radu, Squashed, magnetized black holes in D = 5 minimal gauged supergravity, JHEP 02 (2018) 061 [arXiv:1711.10483] [INSPIRE].
  66. [66]
    D. Cassani and L. Papini, Squashing the boundary of supersymmetric AdS 5 black holes, JHEP 12 (2018) 037 [arXiv:1809.02149] [INSPIRE].
  67. [67]
    A. Bombini and L. Papini, General supersymmetric AdS 5 black holes with squashed boundary, Eur. Phys. J. C 79 (2019) 515 [arXiv:1903.00021] [INSPIRE].
  68. [68]
    D.Z. Freedman and S.S. Pufu, The holography of F -maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.INFN, Sezione di PadovaPadovaItaly
  2. 2.Dipartimento di Fisica e Astronomia “Galileo Galilei”PadovaItaly

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