Advertisement

Journal of High Energy Physics

, 2015:184 | Cite as

Holographic entanglement entropy and the extended phase structure of STU black holes

  • Elena Caceres
  • Phuc H. Nguyen
  • Juan F. Pedraza
Open Access
Regular Article - Theoretical Physics

Abstract

We study the extended thermodynamics, obtained by considering the cosmological constant as a thermodynamic variable, of STU black holes in 4-dimensions in the fixed charge ensemble. The associated phase structure is conjectured to be dual to an RG-flow on the space of field theories. We find that for some charge configurations the phase structure resembles that of a Van der Waals gas: the system exhibits a family of first order phase transitions ending in a second order phase transition at a critical temperature. We calculate the holographic entanglement entropy for several charge configurations and show that for the cases where the gravity background exhibits Van der Waals behavior, the entanglement entropy presents a transition at the same critical temperature. To further characterize the phase transition we calculate appropriate critical exponents and show that they coincide. Thus, the entanglement entropy successfully captures the information of the extended phase structure. Finally, we discuss the physical interpretation of the extended space in terms of the boundary QFT and construct various holographic heat engines dual to STU black holes.

Keywords

Black Holes in String Theory AdS-CFT Correspondence Black Holes 

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]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S.W. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    M. Cvetič and S.S. Gubser, Phases of R charged black holes, spinning branes and strongly coupled gauge theories, JHEP 04 (1999) 024 [hep-th/9902195] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    D. Kastor, S. Ray and J. Traschen, Enthalpy and the mechanics of AdS black holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    B.P. Dolan, Pressure and volume in the first law of black hole thermodynamics, Class. Quant. Grav. 28 (2011) 235017 [arXiv:1106.6260] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    B.P. Dolan, Where is the PdV term in the fist law of black hole thermodynamics?, arXiv:1209.1272 [INSPIRE].
  11. [11]
    D. Kubizňák and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    S.H. Hendi and M.H. Vahidinia, Extended phase space thermodynamics and P-V criticality of black holes with a nonlinear source, Phys. Rev. D 88 (2013) 084045 [arXiv:1212.6128] [INSPIRE].ADSGoogle Scholar
  13. [13]
    D. Kubizňák and R.B. Mann, Black hole chemistry, arXiv:1404.2126 [INSPIRE].
  14. [14]
    W. Xu and L. Zhao, Critical phenomena of static charged AdS black holes in conformal gravity, Phys. Lett. B 736 (2014) 214 [arXiv:1405.7665] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    D. Grumiller, R. McNees and J. Salzer, Cosmological constant as confining U(1) charge in two-dimensional dilaton gravity, Phys. Rev. D 90 (2014) 044032 [arXiv:1406.7007] [INSPIRE].ADSGoogle Scholar
  16. [16]
    B.P. Dolan, Bose condensation and branes, JHEP 10 (2014) 179 [arXiv:1406.7267] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    B.P. Dolan, Black holes and Boyles lawthe thermodynamics of the cosmological constant, Mod. Phys. Lett. A 30 (2015) 1540002 [arXiv:1408.4023] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    A. Rajagopal, D. Kubizňák and R.B. Mann, Van der Waals black hole, Phys. Lett. B 737 (2014) 277 [arXiv:1408.1105] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    J.-L. Zhang, R.-G. Cai and H. Yu, Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS 5× S 5 spacetime, JHEP 02 (2015) 143 [arXiv:1409.5305] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S.H. Hendi, S. Panahiyan and B.E. Panah, P-V criticality and geometrothermodynamics of black holes with Born-Infeld type nonlinear electrodynamics, arXiv:1410.0352 [INSPIRE].
  21. [21]
    H.-H. Zhao, L.-C. Zhang, M.-S. Ma and R. Zhao, Phase transition and Clapeyon equation of black hole in higher dimensional AdS spacetime, arXiv:1411.3554 [INSPIRE].
  22. [22]
    H.-H. Zhao, L.-C. Zhang, M.-S. Ma and R. Zhao, Two phase equilibrium in charged topological dilaton AdS black hole, arXiv:1411.7202 [INSPIRE].
  23. [23]
    T. Delsate and R. Mann, Van der Waals black holes in d dimensions, JHEP 02 (2015) 070 [arXiv:1411.7850] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    J.-L. Zhang, R.-G. Cai and H. Yu, Phase transition and thermodynamical geometry of Reissner-Nordström-AdS black holes in extended phase space, Phys. Rev. D 91 (2015) 044028 [arXiv:1502.01428] [INSPIRE].ADSGoogle Scholar
  25. [25]
    S.H. Hendi and Z. Armanfard, Extended phase space thermodynamics and P-V criticality of charged black holes in Brans-Dicke theory, arXiv:1503.07070 [INSPIRE].
  26. [26]
    C.V. Johnson, Thermodynamic volumes for AdS-Taub-NUT and AdS-Taub-Bolt, Class. Quant. Grav. 31 (2014) 235003 [arXiv:1405.5941] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    C.V. Johnson, The Extended Thermodynamic Phase Structure of Taub-NUT and Taub-Bolt, Class. Quant. Grav. 31 (2014) 225005 [arXiv:1406.4533] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    C.O. Lee, The extended thermodynamic properties of Taub-NUT/Bolt-AdS spaces, Phys. Lett. B 738 (2014) 294 [arXiv:1408.2073] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    R.-G. Cai, L.-M. Cao, L. Li and R.-Q. Yang, P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space, JHEP 09 (2013) 005 [arXiv:1306.6233] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    A.M. Frassino, D. Kubizňák, R.B. Mann and F. Simovic, Multiple reentrant phase transitions and triple points in Lovelock thermodynamics, JHEP 09 (2014) 080 [arXiv:1406.7015] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    B.P. Dolan, A. Kostouki, D. Kubizňák and R.B. Mann, Isolated critical point from Lovelock gravity, Class. Quant. Grav. 31 (2014) 242001 [arXiv:1407.4783] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Z. Sherkatghanad, B. Mirza, Z. Mirzaeyan and S.A.H. Mansoori, Critical behaviors and phase transitions of black holes in higher order gravities and extended phase spaces, arXiv:1412.5028 [INSPIRE].
  33. [33]
    S.H. Hendi, S. Panahiyan and M. Momennia, Extended phase space of AdS black holes in Einstein-Gauss-Bonnet gravity with a quadratic nonlinear electrodynamics, arXiv:1503.03340 [INSPIRE].
  34. [34]
    R.A. Hennigar, W.G. Brenna and R.B. Mann, P-V criticality in quasitopological gravity, JHEP 07 (2015) 077 [arXiv:1505.05517] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    C.V. Johnson, Holographic heat engines, Class. Quant. Grav. 31 (2014) 205002 [arXiv:1404.5982] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  36. [36]
    C.V. Johnson, Large-N phase transitions, finite volume and entanglement entropy, JHEP 03 (2014) 047 [arXiv:1306.4955] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    F. Aprile, D. Rodriguez-Gomez and J.G. Russo, p-wave holographic superconductors and five-dimensional gauged supergravity, JHEP 01 (2011) 056 [arXiv:1011.2172] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    F. Aprile, D. Roest and J.G. Russo, Holographic superconductors from gauged supergravity, JHEP 06 (2011) 040 [arXiv:1104.4473] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    N. Bobev, A. Kundu, K. Pilch and N.P. Warner, Minimal holographic superconductors from maximal supergravity, JHEP 03 (2012) 064 [arXiv:1110.3454] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    M. Cvetič, G.W. Gibbons, D. Kubizňák and C.N. Pope, Black hole enthalpy and an entropy inequality for the thermodynamic volume, Phys. Rev. D 84 (2011) 024037 [arXiv:1012.2888] [INSPIRE].ADSGoogle Scholar
  41. [41]
    K. Behrndt, M. Cvetič and W.A. Sabra, Nonextreme black holes of five-dimensional N = 2 AdS supergravity, Nucl. Phys. B 553 (1999) 317 [hep-th/9810227] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  42. [42]
    M.J. Duff and J.T. Liu, Anti-de Sitter black holes in gauged N = 8 supergravity, Nucl. Phys. B 554 (1999) 237 [hep-th/9901149] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    G.W. Gibbons, M.J. Perry and C.N. Pope, Bulk/boundary thermodynamic equivalence and the Bekenstein and cosmic-censorship bounds for rotating charged AdS black holes, Phys. Rev. D 72 (2005) 084028 [hep-th/0506233] [INSPIRE].ADSMathSciNetGoogle Scholar
  45. [45]
    L. Susskind and E. Witten, The holographic bound in anti-de Sitter space, hep-th/9805114 [INSPIRE].
  46. [46]
    A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev. D 59 (1999) 065011 [hep-th/9809022] [INSPIRE].ADSMathSciNetGoogle Scholar
  47. [47]
    Y. Hatta, E. Iancu, A.H. Mueller and D.N. Triantafyllopoulos, Aspects of the UV/IR correspondence: energy broadening and string fluctuations, JHEP 02 (2011) 065 [arXiv:1011.3763] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  48. [48]
    C.A. Agón, A. Guijosa and J.F. Pedraza, Radiation and a dynamical UV/IR connection in AdS/CFT, JHEP 06 (2014) 043 [arXiv:1402.5961] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    E. Caceres, P.H. Nguyen and J.F. Pedraza, work in progress.Google Scholar
  50. [50]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    F.M. Haehl, T. Hartman, D. Marolf, H. Maxfield and M. Rangamani, Topological aspects of generalized gravitational entropy, JHEP 05 (2015) 023 [arXiv:1412.7561] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    V.E. Hubeny, H. Maxfield, M. Rangamani and E. Tonni, Holographic entanglement plateaux, JHEP 08 (2013) 092 [arXiv:1306.4004] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    E. Caceres, J.F. Pedraza and J. Virrueta, Finite volume effects in holographic entanglement entropy and mutual information, to appear.Google Scholar
  57. [57]
    T. Albash and C.V. Johnson, Holographic studies of entanglement entropy in superconductors, JHEP 05 (2012) 079 [arXiv:1202.2605] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    U. Kol, C. Núñez, D. Schofield, J. Sonnenschein and M. Warschawski, Confinement, phase transitions and non-locality in the entanglement entropy, JHEP 06 (2014) 005 [arXiv:1403.2721] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    G. Georgiou and D. Zoakos, Entanglement entropy of the Klebanov-Strassler model with dynamical flavors, JHEP 07 (2015) 003 [arXiv:1505.01453] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  60. [60]
    S. MacDonald, Thermodynamic volume of Kerr-Bolt-AdS spacetime, arXiv:1406.1257 [INSPIRE].
  61. [61]
    W.G. Brenna, R.B. Mann and M. Park, Mass and thermodynamic volume in Lifshitz spacetimes, Phys. Rev. D 92 (2015) 044015 [arXiv:1505.06331] [INSPIRE].ADSMathSciNetGoogle Scholar
  62. [62]
    D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    E. Caceres and A. Kundu, Holographic thermalization with chemical potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    E. Caceres, A. Kundu, J.F. Pedraza and W. Tangarife, Strong subadditivity, null energy condition and charged black holes, JHEP 01 (2014) 084 [arXiv:1304.3398] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    E. Caceres, A. Kundu, J.F. Pedraza and D.-L. Yang, Weak field collapse in AdS: introducing a charge density, JHEP 06 (2015) 111 [arXiv:1411.1744] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  66. [66]
    A. Bhattacharyya, S. Shajidul Haque and Á. Véliz-Osorio, Renormalized entanglement entropy for BPS black branes, Phys. Rev. D 91 (2015) 045026 [arXiv:1412.2568] [INSPIRE].ADSMathSciNetGoogle Scholar
  67. [67]
    B.P. Dolan, The cosmological constant and the black hole equation of state, Class. Quant. Grav. 28 (2011) 125020 [arXiv:1008.5023] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  68. [68]
    J. Sadeghi and K. Jafarzade, Heat engine of black holes, arXiv:1504.07744 [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Elena Caceres
    • 1
    • 2
  • Phuc H. Nguyen
    • 2
    • 3
  • Juan F. Pedraza
    • 2
    • 3
  1. 1.Facultad de CienciasUniversidad de ColimaColimaMexico
  2. 2.Theory Group, Department of PhysicsUniversity of TexasAustinUnited States
  3. 3.Texas Cosmology CenterUniversity of TexasAustinUnited States

Personalised recommendations