Journal of High Energy Physics

, 2013:74 | Cite as

Quantum corrections to holographic entanglement entropy

Article

Abstract

We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.

Keywords

AdS-CFT Correspondence Black Holes Holography and condensed matter physics (AdS/CMT) 

References

  1. [1]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].MathSciNetGoogle Scholar
  3. [3]
    T. Faulkner, The entanglement Renyi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221 [INSPIRE].
  4. [4]
    T. Hartman, Entanglement entropy at large central charge, arXiv:1303.6955 [INSPIRE].
  5. [5]
    A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    E. Bianchi and R.C. Myers, On the architecture of spacetime geometry, arXiv:1212.5183 [INSPIRE].
  7. [7]
    M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  8. [8]
    L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A quantum source of entropy for black holes, Phys. Rev. D 34 (1986) 373 [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [hep-th/9401070] [INSPIRE].MathSciNetADSGoogle Scholar
  11. [11]
    S.N. Solodukhin, The conical singularity and quantum corrections to entropy of black hole, Phys. Rev. D 51 (1995) 609 [hep-th/9407001] [INSPIRE].MathSciNetADSGoogle Scholar
  12. [12]
    D.V. Fursaev and S.N. Solodukhin, On one loop renormalization of black hole entropy, Phys. Lett. B 365 (1996) 51 [hep-th/9412020] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    J.H. Cooperman and M.A. Luty, Renormalization of entanglement entropy and the gravitational effective action, arXiv:1302.1878 [INSPIRE].
  14. [14]
    S.N. Solodukhin, Entanglement entropy of black holes, Living Rev. Rel. 14 (2011) 8 [arXiv:1104.3712] [INSPIRE].Google Scholar
  15. [15]
    V.P. Frolov, D. Fursaev and A. Zelnikov, Black hole entropy: Off-shell versus on-shell, Phys. Rev. D 54 (1996) 2711 [hep-th/9512184] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    T. Barrella, X. Dong, S.A. Hartnoll and V.L. Martin, Holographic entanglement beyond classical gravity, JHEP 09 (2013) 109 [arXiv:1306.4682] [INSPIRE].Google Scholar
  17. [17]
    V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J. de Boer, M. Kulaxizi and A. Parnachev, Holographic entanglement entropy in Lovelock gravities, JHEP 07 (2011) 109 [arXiv:1101.5781] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    A. Bhattacharyya, A. Kaviraj and A. Sinha, Entanglement entropy in higher derivative holography, JHEP 08 (2013) 012 [arXiv:1305.6694] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    D.V. Fursaev, A. Patrushev and S.N. Solodukhin, Distributional geometry of squashed cones, arXiv:1306.4000 [INSPIRE].
  22. [22]
    A. Sen, Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions, arXiv:1205.0971 [INSPIRE].
  23. [23]
    M. Headrick and T. Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev. D 76 (2007) 106013 [arXiv:0704.3719] [INSPIRE].MathSciNetADSGoogle Scholar
  24. [24]
    I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χ SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    O. Aharony, A note on the holographic interpretation of string theory backgrounds with varying flux, JHEP 03 (2001) 012 [hep-th/0101013] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    S.S. Gubser, C.P. Herzog and I.R. Klebanov, Symmetry breaking and axionic strings in the warped deformed conifold, JHEP 09 (2004) 036 [hep-th/0405282] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].ADSGoogle Scholar
  31. [31]
    M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [INSPIRE].
  32. [32]
    M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [Int. J. Mod. Phys. D 19 (2010) 2429] [arXiv:1005.3035] [INSPIRE].
  33. [33]
    M.M. Wolf et al., Area laws in quantum systems: mutual information and correlations, Phys. Rev. Lett. 100 (2008), no. 7 070502 [arXiv:0704.3906].
  34. [34]
    H. Casini and M. Huerta, Remarks on the entanglement entropy for disconnected regions, JHEP 03 (2009) 048 [arXiv:0812.1773] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory II, J. Stat. Mech. 1101 (2011) P01021 [arXiv:1011.5482] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  36. [36]
    J. Cardy, Some results on the mutual information of disjoint regions in higher dimensions, J. Phys. A 46 (2013) 285402 [arXiv:1304.7985] [INSPIRE].MathSciNetGoogle Scholar
  37. [37]
    J. Molina-Vilaplana, On the mutual information between disconnected regions in AdS/CFT, arXiv:1305.1064 [INSPIRE].
  38. [38]
    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].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  40. [40]
    H. Araki and E. Lieb, Entropy inequalities, Commun. Math. Phys. 18 (1970) 160 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  41. [41]
    V.E. Hubeny, H. Maxfield, M. Rangamani and E. Tonni, Holographic entanglement plateaux, JHEP 08 (2013) 092 [arXiv:1306.4004] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative entropy and holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    M.M. Wolf, Violation of the entropic area law for Fermions, Phys. Rev. Lett. 96 (2006) 010404 [quant-ph/0503219] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    D. Gioev and I. Klich, Entanglement entropy of Fermions in any dimension and the widom conjecture, Phys. Rev. Lett. 96 (2006) 100503 [quant-ph/0504151].MathSciNetADSCrossRefGoogle Scholar
  45. [45]
    T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].ADSGoogle Scholar
  46. [46]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].ADSGoogle Scholar
  47. [47]
    S. Sachdev, A model of a Fermi liquid using gauge-gravity duality, Phys. Rev. D 84 (2011) 066009 [arXiv:1107.5321] [INSPIRE].ADSGoogle Scholar
  48. [48]
    N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Thomas Faulkner
    • 1
  • Aitor Lewkowycz
    • 2
  • Juan Maldacena
    • 1
  1. 1.Institute for Advanced StudyPrincetonU.S.A.
  2. 2.Jadwin HallPrinceton UniversityPrincetonU.S.A.

Personalised recommendations