Journal of High Energy Physics

, 2016:65 | Cite as

Correlators at large c without information loss

  • Andrea Galliani
  • Stefano Giusto
  • Emanuele Moscato
  • Rodolfo Russo
Open Access
Regular Article - Theoretical Physics

Abstract

We study a simple class of correlators with two heavy and two light operators both in the D1D5 CFT and in the dual AdS3 × S3 × T4 description. On the CFT side we focus on the free orbifold point and discuss how these correlators decompose in terms of conformal blocks, showing that they are determined by protected quantities. On the gravity side, the heavy states are described by regular, asymptotically AdS3 × S3 × T4 solutions and the correlators are obtained by studying the wave equation in these backgrounds. We find that the CFT and the gravity results agree and that, even in the large central charge limit, these correlators do not have (Euclidean) spurious singularities. We suggest that this is indeed a general feature of the heavy-light correlators in unitary CFTs, which can be relevant for understanding how information is encoded in black hole microstates.

Keywords

AdS-CFT Correspondence Black Holes in String Theory Conformal Field Models in String Theory 

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].MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    R. Dijkgraaf, Instanton strings and hyper-Kähler geometry, Nucl. Phys. B 543 (1999) 545 [hep-th/9810210] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    F. Larsen and E.J. Martinec, U(1) charges and moduli in the D1-D5 system, JHEP 06 (1999) 019 [hep-th/9905064] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A. Jevicki, M. Mihailescu and S. Ramgoolam, Gravity from CFT on S N (X): symmetries and interactions, Nucl. Phys. B 577 (2000) 47 [hep-th/9907144] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    K. Skenderis and M. Taylor, Kaluza-Klein holography, JHEP 05 (2006) 057 [hep-th/0603016] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    K. Skenderis and M. Taylor, Holographic Coulomb branch vevs, JHEP 08 (2006) 001 [hep-th/0604169] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    K. Skenderis and M. Taylor, Fuzzball solutions and D1-D5 microstates, Phys. Rev. Lett. 98 (2007) 071601 [hep-th/0609154] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    I. Kanitscheider, K. Skenderis and M. Taylor, Holographic anatomy of fuzzballs, JHEP 04 (2007) 023 [hep-th/0611171] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    S. Giusto, E. Moscato and R. Russo, AdS 3 holography for 1/4 and 1/8 BPS geometries, JHEP 11 (2015) 004 [arXiv:1507.00945] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].MathSciNetMATHGoogle Scholar
  13. [13]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    C.T. Asplund and S.G. Avery, Evolution of entanglement entropy in the D1-D5 brane system, Phys. Rev. D 84 (2011) 124053 [arXiv:1108.2510] [INSPIRE].ADSGoogle Scholar
  16. [16]
    J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical property of entanglement entropy for excited states, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    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
  18. [18]
    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
  19. [19]
    P.A.R. Jones and M. Taylor, Entanglement entropy in top-down models, JHEP 08 (2016) 158 [arXiv:1602.04825] [INSPIRE].CrossRefGoogle Scholar
  20. [20]
    J.R. David, S. Khetrapal and S.P. Kumar, Universal corrections to entanglement entropy of local quantum quenches, JHEP 08 (2016) 127 [arXiv:1605.05987] [INSPIRE].CrossRefGoogle Scholar
  21. [21]
    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].MathSciNetGoogle Scholar
  22. [22]
    S. Giusto and R. Russo, Entanglement entropy and D1-D5 geometries, Phys. Rev. D 90 (2014) 066004 [arXiv:1405.6185] [INSPIRE].ADSGoogle Scholar
  23. [23]
    M.J.S. Beach, J. Lee, C. Rabideau and M. Van Raamsdonk, Entanglement entropy from one-point functions in holographic states, JHEP 06 (2016) 085 [arXiv:1604.05308] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    O. Lunin and S.D. Mathur, A toy black hole S-matrix in the D1-D5 CFT, JHEP 02 (2013) 083 [arXiv:1211.5830] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    K. Goto, M. Miyaji and T. Takayanagi, Causal evolutions of bulk local excitations from CFT, arXiv:1605.02835 [INSPIRE].
  26. [26]
    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
  27. [27]
    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
  28. [28]
    E. Hijano, P. Kraus and R. Snively, Worldline approach to semi-classical conformal blocks, JHEP 07 (2015) 131 [arXiv:1501.02260] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    K.B. Alkalaev and V.A. Belavin, Classical conformal blocks via AdS/CFT correspondence, JHEP 08 (2015) 049 [arXiv:1504.05943] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Semiclassical Virasoro blocks from AdS 3 gravity, JHEP 12 (2015) 077 [arXiv:1508.04987] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten diagrams revisited: the AdS geometry of conformal blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    B. Carneiro da Cunha and M. Guica, Exploring the BTZ bulk with boundary conformal blocks, arXiv:1604.07383 [INSPIRE].
  33. [33]
    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
  34. [34]
    E. Perlmutter, Virasoro conformal blocks in closed form, JHEP 08 (2015) 088 [arXiv:1502.07742] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    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
  36. [36]
    A.L. Fitzpatrick and J. Kaplan, Conformal blocks beyond the semi-classical limit, JHEP 05 (2016) 075 [arXiv:1512.03052] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    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].ADSCrossRefGoogle Scholar
  38. [38]
    S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  39. [39]
    S.D. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [INSPIRE].
  40. [40]
    S.G. Avery, Using the D1-D5 CFT to understand black holes, arXiv:1012.0072 [INSPIRE].
  41. [41]
    V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S.F. Ross, Supersymmetric conical defects: towards a string theoretic description of black hole formation, Phys. Rev. D 64 (2001) 064011 [hep-th/0011217] [INSPIRE].ADSMathSciNetGoogle Scholar
  42. [42]
    J.M. Maldacena and L. Maoz, Desingularization by rotation, JHEP 12 (2002) 055 [hep-th/0012025] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    P. Caputa, T. Numasawa and A. Veliz-Osorio, Scrambling without chaos in RCFT, arXiv:1602.06542 [INSPIRE].
  44. [44]
    P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer, Germany (1997).Google Scholar
  45. [45]
    V.G. Knizhnik and A.B. Zamolodchikov, Current algebra and Wess-Zumino model in two-dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].
  48. [48]
    S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  49. [49]
    I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].ADSMathSciNetGoogle Scholar
  50. [50]
    P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  51. [51]
    J. Ford, S. Giusto and A. Saxena, A class of BPS time-dependent 3-charge microstates from spectral flow, Nucl. Phys. B 790 (2008) 258 [hep-th/0612227] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    O. Lunin, S.D. Mathur and D. Turton, Adding momentum to supersymmetric geometries, Nucl. Phys. B 868 (2013) 383 [arXiv:1208.1770] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  53. [53]
    S. Giusto, O. Lunin, S.D. Mathur and D. Turton, D1-D5-P microstates at the cap, JHEP 02 (2013) 050 [arXiv:1211.0306] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    I. Bena, E. Martinec, D. Turton and N.P. Warner, Momentum fractionation on superstrata, JHEP 05 (2016) 064 [arXiv:1601.05805] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [INSPIRE].ADSMathSciNetGoogle Scholar
  57. [57]
    B. Chakrabarty, D. Turton and A. Virmani, Holographic description of non-supersymmetric orbifolded D1-D5-P solutions, JHEP 11 (2015) 063 [arXiv:1508.01231] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    S. Deger, A. Kaya, E. Sezgin and P. Sundell, Spectrum of D = 6, N = 4b supergravity on AdS in three-dimensions ×S 3, Nucl. Phys. B 536 (1998) 110 [hep-th/9804166] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  59. [59]
    S.D. Mathur, A. Saxena and Y.K. Srivastava, Constructing ‘hair’ for the three charge hole, Nucl. Phys. B 680 (2004) 415 [hep-th/0311092] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  60. [60]
    M. Shigemori, Perturbative 3-charge microstate geometries in six dimensions, JHEP 10 (2013) 169 [arXiv:1307.3115] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  61. [61]
    K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP 05 (2009) 085 [arXiv:0812.2909] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    I. Ya. Aref’eva and M.A. Khramtsov, AdS/CFT prescription for angle-deficit space and winding geodesics, JHEP 04 (2016) 121 [arXiv:1601.02008] [INSPIRE].
  63. [63]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  64. [64]
    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
  65. [65]
    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  66. [66]
    S.D. Mathur and C.J. Plumberg, Correlations in Hawking radiation and the infall problem, JHEP 09 (2011) 093 [arXiv:1101.4899] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  67. [67]
    S.D. Mathur and D. Turton, Comments on black holes I: the possibility of complementarity, JHEP 01 (2014) 034 [arXiv:1208.2005] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  68. [68]
    M.R. Gaberdiel and R. Gopakumar, Higher spins & strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  69. [69]
    M.R. Gaberdiel, C. Peng and I.G. Zadeh, Higgsing the stringy higher spin symmetry, JHEP 10 (2015) 101 [arXiv:1506.02045] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  70. [70]
    M.R. Gaberdiel and R. Gopakumar, String theory as a higher spin theory, arXiv:1512.07237 [INSPIRE].
  71. [71]
    V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk versus boundary dynamics in Anti-de Sitter space-time, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [INSPIRE].ADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Andrea Galliani
    • 1
    • 2
  • Stefano Giusto
    • 1
    • 2
  • Emanuele Moscato
    • 3
  • Rodolfo Russo
    • 3
  1. 1.Dipartimento di Fisica ed Astronomia “Galileo Galilei”Università di PadovaPadovaItaly
  2. 2.INFN — Sezione di PadovaPadovaItaly
  3. 3.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonU.K.

Personalised recommendations