Advertisement

Journal of High Energy Physics

, 2018:96 | Cite as

Modular Hamiltonians and large diffeomorphisms in AdS3

  • Suchetan Das
  • Bobby EzhuthachanEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We generalize the work of Kabat and Lifshytz (arXiv:1703.06523), of reconstructing bulk scalar fields using the intersecting modular Hamiltonian approach discussed therein, to any locally AdS3 space related to AdS3 by large diffeomorphisms. We present several checks for our result including matching with their result in appropriate limits as well as consistency with bulk diffeomorphisms. As a further check, from our expressions we also compute the first correction due to gravitational dressing to the bulk scalar field in AdS3 and match with known results in the literature.

Keywords

AdS-CFT Correspondence Conformal Field Theory 

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].CrossRefzbMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].
  6. [6]
    A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
  7. [7]
    A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Holographic description of the black hole interior, Phys. Rev. D 75 (2007) 106001 [Erratum ibid. D 75 (2007) 129902] [hep-th/0612053] [INSPIRE].
  8. [8]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  10. [10]
    A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].CrossRefzbMATHGoogle Scholar
  12. [12]
    D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    X. Dong, D. Harlow and A.C. Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
  15. [15]
    D. Harlow, The Ryu-Takayanagi Formula from Quantum Error Correction, Commun. Math. Phys. 354 (2017) 865 [arXiv:1607.03901] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    D. Harlow, TASI Lectures on the Emergence of Bulk Physics in AdS/CFT, PoS(TASI2017)002 (2018) [arXiv:1802.01040] [INSPIRE].
  17. [17]
    D. Kabat and G. Lifschytz, Local bulk physics from intersecting modular Hamiltonians, JHEP 06 (2017) 120 [arXiv:1703.06523] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    F. Sanches and S.J. Weinberg, Boundary dual of bulk local operators, Phys. Rev. D 96 (2017) 026004 [arXiv:1703.07780] [INSPIRE].
  19. [19]
    T. Faulkner and A. Lewkowycz, Bulk locality from modular flow, JHEP 07 (2017) 151 [arXiv:1704.05464] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    E. Witten, APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys. 90 (2018) 045003 [arXiv:1803.04993] [INSPIRE].
  21. [21]
    B. Czech, L. Lamprou, S. McCandlish, B. Mosk and J. Sully, A Stereoscopic Look into the Bulk, JHEP 07 (2016) 129 [arXiv:1604.03110] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    A. Lewkowycz, G.J. Turiaci and H. Verlinde, A CFT Perspective on Gravitational Dressing and Bulk Locality, JHEP 01 (2017) 004 [arXiv:1608.08977] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    M. Guica, Bulk fields from the boundary OPE, arXiv:1610.08952 [INSPIRE].
  24. [24]
    P.D. Hislop and R. Longo, Modular Structure of the Local Algebras Associated With the Free Massless Scalar Field Theory, Commun. Math. Phys. 84 (1982) 71 [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal field theory, J. Stat. Mech. 1612 (2016) 123103 [arXiv:1608.01283] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  27. [27]
    N. Anand, H. Chen, A.L. Fitzpatrick, J. Kaplan and D. Li, An Exact Operator That Knows Its Location, JHEP 02 (2018) 012 [arXiv:1708.04246] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    M. Bañados, Three-dimensional quantum geometry and black holes, AIP Conf. Proc. 484 (1999) 147 [hep-th/9901148] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    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 [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    M.M. Roberts, Time evolution of entanglement entropy from a pulse, JHEP 12 (2012) 027 [arXiv:1204.1982] [INSPIRE].CrossRefGoogle Scholar
  31. [31]
    Y. Chen, X. Dong, A. Lewkowycz and X.-L. Qi, Modular Flow as a Disentangler, arXiv:1806.09622 [INSPIRE].
  32. [32]
    T. Faulkner, M. Li and H. Wang, A modular toolkit for bulk reconstruction, arXiv:1806.10560 [INSPIRE].
  33. [33]
    T. Faulkner, Entanglement Entropy and Quantum Fields, parts I, II & III, lectures at “It from Qubit” School, Instituto Balseiro, Centro Atómico Bariloche [https://www.youtube.com/watch?v=RDxKJiB1AIk&t=3548s] [https://www.youtube.com/watch?v=WappEuCnLBs] [https://www.youtube.com/watch?v=Ug7ZtPgw6W8&t=3529s].
  34. [34]
    S.R. Roy and D. Sarkar, Bulk metric reconstruction from boundary entanglement, Phys. Rev. D 98 (2018) 066017 [arXiv:1801.07280] [INSPIRE].
  35. [35]
    D. Kabat, G. Lifschytz and D.A. Lowe, Constructing local bulk observables in interacting AdS/CFT, Phys. Rev. D 83 (2011) 106009 [arXiv:1102.2910] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Ramakrishna Mission Vivekananda Educational and Research InstituteHowrahIndia

Personalised recommendations