Advertisement

The bulk-to-boundary propagator in black hole microstate backgrounds

  • Hongbin ChenEmail author
  • A. Liam Fitzpatrick
  • Jared Kaplan
  • Daliang Li
Open Access
Regular Article - Theoretical Physics

Abstract

First-quantized propagation in quantum gravitational AdS3 backgrounds can be exactly reconstructed using CFT2 data and Virasoro symmetry. We develop methods to compute the bulk-to-boundary propagator in a black hole microstate, \( \left\langle {\phi}_L{\mathcal{O}}_L{\mathcal{O}}_H{\mathcal{O}}_H\right\rangle \), at finite central charge. As a first application, we show that the semiclassical theory on the Euclidean BTZ solution sharply disagrees with the exact description, as expected based on the resolution of forbidden thermal singularities, though this effect may appear exponentially small for physical observers.

Keywords

1/N Expansion AdS-CFT Correspondence Black Holes 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.

Supplementary material

13130_2019_10785_MOESM1_ESM.nb (228 kb)
ESM 1 (NB 227 kb)

References

  1. [1]
    T. Hartman, Entanglement entropy at large central charge, arXiv:1303.6955 [INSPIRE].
  2. [2]
    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
  3. [3]
    A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of long-distance AdS physics from the CFT bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Virasoro conformal blocks and thermality from classical background fields, JHEP 11 (2015) 200 [arXiv:1501.05315] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    A.L. Fitzpatrick, J. Kaplan, M.T. Walters and J. Wang, Hawking from Catalan, JHEP 05 (2016) 069 [arXiv:1510.00014] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    T. Anous, T. Hartman, A. Rovai and J. Sonner, Black hole collapse in the 1/c expansion, JHEP 07 (2016) 123 [arXiv:1603.04856] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Entanglement scrambling in 2d conformal field theory, JHEP 09 (2015) 110 [arXiv:1506.03772] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic entanglement entropy from 2d CFT: heavy states and local quenches, JHEP 02 (2015) 171 [arXiv:1410.1392] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    P. Caputa, J. Simón, A. Štikonas and T. Takayanagi, Quantum entanglement of localized excited states at finite temperature, JHEP 01 (2015) 102 [arXiv:1410.2287] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Beccaria, A. Fachechi and G. Macorini, Virasoro vacuum block at next-to-leading order in the heavy-light limit, JHEP 02 (2016) 072 [arXiv:1511.05452] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    E. Hijano, P. Kraus and R. Snively, Worldline approach to semi-classical conformal blocks, JHEP 07 (2015) 131 [arXiv:1501.02260] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Semiclassical Virasoro blocks from AdS 3 gravity, JHEP 12 (2015) 077 [arXiv:1508.04987] [INSPIRE].ADSzbMATHGoogle Scholar
  14. [14]
    K.B. Alkalaev and V.A. Belavin, Classical conformal blocks via AdS/CFT correspondence, JHEP 08 (2015) 049 [arXiv:1504.05943] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    K.B. Alkalaev and V.A. Belavin, Monodromic vs. geodesic computation of Virasoro classical conformal blocks, Nucl. Phys. B 904 (2016) 367 [arXiv:1510.06685] [INSPIRE].
  16. [16]
    B. Chen, J.-q. Wu and J.-j. Zhang, Holographic description of 2D conformal block in semi-classical limit, JHEP 10 (2016) 110 [arXiv:1609.00801] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    N. Lashkari, A. Dymarsky and H. Liu, Universality of quantum information in chaotic CFTs, JHEP 03 (2018) 070 [arXiv:1710.10458] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    H. Maxfield, A view of the bulk from the worldline, arXiv:1712.00885 [INSPIRE].
  19. [19]
    Y. Kusuki, Large c Virasoro blocks from monodromy method beyond known limits, JHEP 08 (2018) 161 [arXiv:1806.04352] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    Y. Hikida and T. Uetoko, Conformal blocks from Wilson lines with loop corrections, Phys. Rev. D 97 (2018) 086014 [arXiv:1801.08549] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  21. [21]
    P. Kraus, A. Sivaramakrishnan and R. Snively, Black holes from CFT: universality of correlators at large c, JHEP 08 (2017) 084 [arXiv:1706.00771] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    J. Cotler and K. Jensen, A theory of reparameterizations for AdS 3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, On information loss in AdS 3 /CFT 2, JHEP 05 (2016) 109 [arXiv:1603.08925] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    H. Chen, C. Hussong, J. Kaplan and D. Li, A numerical approach to virasoro blocks and the information paradox, JHEP 09 (2017) 102 [arXiv:1703.09727] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    Y. Kusuki, New properties of large-c conformal blocks from recursion relation, JHEP 07 (2018) 010 [arXiv:1804.06171] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    A.L. Fitzpatrick and J. Kaplan, On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles, JHEP 04 (2017) 072 [arXiv:1609.07153] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    Y. Kusuki, Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity, JHEP 01 (2019) 025 [arXiv:1810.01335] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    P. Kraus, A. Sivaramakrishnan and R. Snively, Late time Wilson lines, JHEP 04 (2019) 026 [arXiv:1810.01439] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    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].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    H. Chen, A.L. Fitzpatrick, J. Kaplan and D. Li, The AdS 3 propagator and the fate of locality, JHEP 04 (2018) 075 [arXiv:1712.02351] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    V. Balasubramanian et al., Typicality versus thermality: an analytic distinction, Gen. Rel. Grav. 40 (2008) 1863 [hep-th/0701122] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    H. Liu, Scattering in Anti-de Sitter space and operator product expansion, Phys. Rev. D 60 (1999) 106005 [hep-th/9811152] [INSPIRE].ADSGoogle Scholar
  33. [33]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    A.L. Fitzpatrick and J. Kaplan, Unitarity and the holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE convergence in conformal field theory, Phys. Rev. D 86 (2012) 105043 [arXiv:1208.6449] [INSPIRE].ADSGoogle Scholar
  36. [36]
    T. Hartman, C.A. Keller and B. Stoica, Universal spectrum of 2d conformal field theory in the large c limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    J. Cardy, A. Maloney and H. Maxfield, A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance, JHEP 10 (2017) 136 [arXiv:1705.05855] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    A.L. Fitzpatrick and J. Kaplan, AdS field theory from conformal field theory, JHEP 02 (2013) 054 [arXiv:1208.0337] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    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].ADSMathSciNetGoogle Scholar
  40. [40]
    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].ADSGoogle Scholar
  41. [41]
    D. Kabat and G. Lifschytz, Locality, bulk equations of motion and the conformal bootstrap, JHEP 10 (2016) 091 [arXiv:1603.06800] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    A. Zamolodchikov, Conformal symmetry in two-dimensions: an explicit recurrence formula for the conformal partial wave amplitude, Commun. Math. Phys. 96 (1984) 419.ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    A. Zamolodchikov, Conformal symmetry in two-dimensional space: recursion representation of the conformal block, Teor. Mat. Fiz. 73 (1987) 103.CrossRefGoogle Scholar
  44. [44]
    B. Czech et al., A stereoscopic look into the bulk, JHEP 07 (2016) 129 [arXiv:1604.03110] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, Exact virasoro blocks from Wilson lines and background-independent operators, JHEP 07 (2017) 092 [arXiv:1612.06385] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    M. Besken, E. D’Hoker, A. Hegde and P. Kraus, Renormalization of gravitational Wilson lines, JHEP 06 (2019) 020 [arXiv:1810.00766] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    E. Keski-Vakkuri, Bulk and boundary dynamics in BTZ black holes, Phys. Rev. D 59 (1999) 104001 [hep-th/9808037] [INSPIRE].ADSMathSciNetGoogle Scholar
  48. [48]
    T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
  49. [49]
    I. Bena, On the construction of local fields in the bulk of AdS 5 and other spaces, Phys. Rev. D 62 (2000) 066007 [hep-th/9905186] [INSPIRE].ADSMathSciNetGoogle Scholar
  50. [50]
    H. Verlinde, Poking holes in AdS/CFT: bulk fields from boundary states, arXiv:1505.05069 [INSPIRE].
  51. [51]
    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].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    M.M. Roberts, Time evolution of entanglement entropy from a pulse, JHEP 12 (2012) 027 [arXiv:1204.1982] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    D. Harlow, J. Maltz and E. Witten, Analytic continuation of Liouville theory, JHEP 12 (2011) 071 [arXiv:1108.4417] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP 01 (2017) 013 [arXiv:1509.03612] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    E. Perlmutter, Virasoro conformal blocks in closed form, JHEP 08 (2015) 088 [arXiv:1502.07742] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    M. Cho, S. Collier and X. Yin, Recursive representations of arbitrary Virasoro conformal blocks, JHEP 04 (2019) 018 [arXiv:1703.09805] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    K.B. Alkalaev and V.A. Belavin, From global to heavy-light: 5-point conformal blocks, JHEP 03 (2016) 184 [arXiv:1512.07627] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    A.L. Fitzpatrick and J. Kaplan, Conformal blocks beyond the semi-classical limit, JHEP 05 (2016) 075 [arXiv:1512.03052] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The analytic bootstrap and AdS superhorizon locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  60. [60]
    Z. Komargodski and A. Zhiboedov, Convexity and liberation at large spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: how to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreU.S.A.
  2. 2.Department of PhysicsBoston UniversityBostonU.S.A.

Personalised recommendations