Quantum corrections to holographic mutual information

  • Cesar A. AgónEmail author
  • Thomas Faulkner
Open Access
Regular Article - Theoretical Physics


We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expansion method introduced by Cardy [1]. For CFTs with holographic duals the leading contribution to the MI at long distances comes from bulk quantum corrections to the Ryu-Takayanagi area formula. According to the FLM proposal [2] this equals the bulk MI between the two disjoint regions spanned by the boundary spheres and their corresponding minimal area surfaces. We compute this quantum correction and provide in this way a non-trivial check of the FLM proposal.


AdS-CFT Correspondence Field Theories in Higher Dimensions 


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.


  1. [1]
    J. Cardy, Some results on the mutual information of disjoint regions in higher dimensions, J. Phys. A 46 (2013) 285402 [arXiv:1304.7985] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  2. [2]
    T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Headrick, Entanglement Rényi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].ADSGoogle Scholar
  4. [4]
    B. Swingle, L. Huijse and S. Sachdev, Entanglement entropy of compressible holographic matter: loop corrections from bulk fermions, Phys. Rev. B 90 (2014) 045107 [arXiv:1308.3234] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    S. Leichenauer, Thermal corrections to entanglement entropy from holography, JHEP 09 (2015) 014 [arXiv:1502.07348] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  6. [6]
    B. Swingle and M. Van Raamsdonk, Universality of gravity from entanglement, arXiv:1405.2933 [INSPIRE].
  7. [7]
    T. Miyagawa, N. Shiba and T. Takayanagi, Double-trace deformations and entanglement entropy in AdS, Fortsch. Phys. 64 (2016) 92 [arXiv:1511.07194] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    N. Engelhardt and A.C. Wall, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T. Barrella, X. Dong, S.A. Hartnoll and V.L. Martin, Holographic entanglement beyond classical gravity, JHEP 09 (2013) 109 [arXiv:1306.4682] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  10. [10]
    T. Faulkner, The entanglement Rényi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221 [INSPIRE].
  11. [11]
    B. Chen, J.-Q. Wu and Z.-C. Zheng, Holographic Rényi entropy of single interval on torus: with W symmetry, Phys. Rev. D 92 (2015) 066002 [arXiv:1507.00183] [INSPIRE].ADSGoogle Scholar
  12. [12]
    B. Chen and J.-Q. Wu, Holographic calculation for large interval Rényi entropy at high temperature, Phys. Rev. D 92 (2015) 106001 [arXiv:1506.03206] [INSPIRE].ADSGoogle Scholar
  13. [13]
    B. Chen and J.-Q. Wu, Large interval limit of Rényi entropy at high temperature, Phys. Rev. D 92 (2015) 126002 [arXiv:1412.0763] [INSPIRE].ADSGoogle Scholar
  14. [14]
    B. Chen and J.-Q. Wu, Single interval Rényi entropy at low temperature, JHEP 08 (2014) 032 [arXiv:1405.6254] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    M. Beccaria and G. Macorini, On the next-to-leading holographic entanglement entropy in AdS 3 /CFT 2, JHEP 04 (2014) 045 [arXiv:1402.0659] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    B. Chen, F.-Y. Song and J.-J. Zhang, Holographic Rényi entropy in AdS 3 /LCFT 2 correspondence, JHEP 03 (2014) 137 [arXiv:1401.0261] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    B. Chen and J.-J. Zhang, On short interval expansion of Rényi entropy, JHEP 11 (2013) 164 [arXiv:1309.5453] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    B. Chen, J. Long and J.-J. Zhang, Holographic Rényi entropy for CFT with W symmetry, JHEP 04 (2014) 041 [arXiv:1312.5510] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    E. Perlmutter, Comments on Rényi entropy in AdS 3 /CFT 2, JHEP 05 (2014) 052 [arXiv:1312.5740] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    N. Shiba, Entanglement entropy of two spheres, JHEP 07 (2012) 100 [arXiv:1201.4865] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory II, J. Stat. Mech. 01 (2011) P01021 [arXiv:1011.5482] [INSPIRE].MathSciNetGoogle Scholar
  22. [22]
    H.J. Schnitzer, Mutual Rényi information for two disjoint compound systems, arXiv:1406.1161 [INSPIRE].
  23. [23]
    C.P. Herzog, Universal thermal corrections to entanglement entropy for conformal field theories on spheres, JHEP 10 (2014) 028 [arXiv:1407.1358] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    C.P. Herzog and J. Nian, Thermal corrections to Rényi entropies for conformal field theories, JHEP 06 (2015) 009 [arXiv:1411.6505] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    C.A. Agón, I. Cohen-Abbo and H.J. Schnitzer, Large distance expansion of mutual information for disjoint disks in a free scalar theory, arXiv:1505.03757 [INSPIRE].
  26. [26]
    C.P. Herzog and M. Spillane, Thermal corrections to Rényi entropies for free fermions, JHEP 04 (2016) 124 [arXiv:1506.06757] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    T. Faulkner, Bulk emergence and the RG flow of entanglement entropy, JHEP 05 (2015) 033 [arXiv:1412.5648] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    T. Faulkner, R.G. Leigh and O. Parrikar, Shape dependence of entanglement entropy in conformal field theories, JHEP 04 (2016) 088 [arXiv:1511.05179] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in Strings, branes and extra dimensions: TASI 2001: proceedings, U.S.A. (2001), pg. 3 [hep-th/0201253] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Martin Fisher School of PhysicsBrandeis UniversityWalthamUSA
  2. 2.University of IllinoisUrbana-ChampaignUrbanaUSA

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