AdS/CFT prescription for angle-deficit space and winding geodesics

  • Irina Ya. Aref’eva
  • Mikhail A. KhramtsovEmail author
Open Access
Regular Article - Theoretical Physics


We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS3 space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical bulk-boundary propagator for a scalar field in the space with conical defect and use it to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of \( {\mathrm{\mathbb{Z}}}_r \)-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.


AdS-CFT Correspondence Gauge-gravity correspondence 


Open Access

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  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].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle 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].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
  6. [6]
    I. Ya. Aref’eva, Holographic approach to quark-gluon plasma in heavy ion collisions, Phys. Usp. 57 (2014) 527.Google Scholar
  7. [7]
    O. DeWolfe, S.S. Gubser, C. Rosen and D. Teaney, Heavy ions and string theory, Prog. Part. Nucl. Phys. 75 (2014) 86 [arXiv:1304.7794] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    S. Sachdev, Condensed Matter and AdS/CFT, Lect. Notes Phys. 828 (2011) 273 [arXiv:1002.2947] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  10. [10]
    I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Langevin diffusion of heavy quarks in non-conformal holographic backgrounds, JHEP 12 (2010) 088 [arXiv:1006.3261] [INSPIRE].CrossRefzbMATHGoogle Scholar
  12. [12]
    U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].CrossRefGoogle Scholar
  14. [14]
    A. Buchel, J.G. Russo and K. Zarembo, Rigorous Test of Non-conformal Holography: Wilson Loops in N = 2* Theory, JHEP 03 (2013) 062 [arXiv:1301.1597] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].ADSGoogle Scholar
  16. [16]
    J. Aparicio and E. Lopez, Evolution of Two-Point Functions from Holography, JHEP 12 (2011) 082 [arXiv:1109.3571] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    V. Keranen, E. Keski-Vakkuri and L. Thorlacius, Thermalization and entanglement following a non-relativistic holographic quench, Phys. Rev. D 85 (2012) 026005 [arXiv:1110.5035] [INSPIRE].ADSGoogle Scholar
  18. [18]
    E. Caceres and A. Kundu, Holographic Thermalization with Chemical Potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    V. Balasubramanian et al., Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP 04 (2013) 069 [arXiv:1212.6066] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    I. Ya. Aref’eva, A. Bagrov and A.S. Koshelev, Holographic Thermalization from Kerr-AdS, JHEP 07 (2013) 170 [arXiv:1305.3267] [INSPIRE].
  21. [21]
    I. Ya. Aref’eva, QGP time formation in holographic shock waves model of heavy ion collisions, arXiv:1503.02185 [INSPIRE].
  22. [22]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    R. Callan, J.-Y. He and M. Headrick, Strong subadditivity and the covariant holographic entanglement entropy formula, JHEP 06 (2012) 081 [arXiv:1204.2309] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    V. Balasubramanian, B.D. Chowdhury, B. Czech and J. de Boer, Entwinement and the emergence of spacetime, JHEP 01 (2015) 048 [arXiv:1406.5859] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, arXiv:1503.01409 [INSPIRE].
  27. [27]
    V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].ADSMathSciNetGoogle Scholar
  28. [28]
    V.E. Hubeny and M. Rangamani, A Holographic view on physics out of equilibrium, Adv. High Energy Phys. 2010 (2010) 297916 [arXiv:1006.3675] [INSPIRE].CrossRefzbMATHGoogle Scholar
  29. [29]
    T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    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
  31. [31]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    S. Deser, R. Jackiw and G. ’t Hooft, Three-dimensional Einstein gravity: dynamics of flat space, Annals Phys. 152 (1984) 220 [INSPIRE].
  33. [33]
    S. Deser and R. Jackiw, Three-Dimensional Cosmological Gravity: Dynamics of Constant Curvature, Annals Phys. 153 (1984) 405 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    S. Deser and R. Jackiw, Classical and Quantum Scattering on a Cone, Commun. Math. Phys. 118 (1988) 495.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    G. ’t Hooft, Quantization of point particles in (2 + 1)-dimensional gravity and space-time discreteness, Class. Quant. Grav. 13 (1996) 1023 [gr-qc/9601014] [INSPIRE].
  36. [36]
    I. Ya. Arefeva and A.A. Bagrov, Holographic dual of a conical defect, Theor. Math. Phys. 182 (2015) 1 [INSPIRE].
  37. [37]
    I. Ya. Arefeva, A. Bagrov, P. Saterskog and K. Schalm, Holographic dual of a time machine, arXiv:1508.04440 [INSPIRE].
  38. [38]
    D.S. Ageev, I. Ya. Aref’eva and M.D. Tikhanovskaya, Holographic Dual to Conical Defects: I. Moving Massive Particle, arXiv:1512.03362 [INSPIRE].
  39. [39]
    D.S. Ageev and I. Ya. Aref’eva, Holographic Dual to Conical Defects: II. Colliding Ultrarelativistic Particles, arXiv:1512.03363 [INSPIRE].
  40. [40]
    J.M. Izquierdo and P.K. Townsend, Supersymmetric space-times in (2 + 1) AdS supergravity models, Class. Quant. Grav. 12 (1995) 895 [gr-qc/9501018] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    J.S. Dowker, Quantum Field Theory on a Cone, J. Phys. A 10 (1977) 115 [INSPIRE].ADSMathSciNetGoogle Scholar
  42. [42]
    M.O. Katanaev and I.V. Volovich, Theory of defects in solids and three-dimensional gravity, Annals Phys. 216 (1992) 1 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    C.A.B. Bayona, C.N. Ferreira and V.J.V. Otoya, A Conical deficit in the AdS 4 /CFT 3 correspondence, Class. Quant. Grav. 28 (2011) 015011 [arXiv:1003.5396] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  44. [44]
    M. Smolkin and S.N. Solodukhin, Correlation functions on conical defects, Phys. Rev. D 91 (2015) 044008 [arXiv:1406.2512] [INSPIRE].ADSGoogle Scholar
  45. [45]
    T.W.B. Kibble, Topology of Cosmic Domains and Strings, J. Phys. A 9 (1976) 1387 [INSPIRE].ADSzbMATHGoogle Scholar
  46. [46]
    I. Ya. Aref’eva, Colliding Hadrons as Cosmic Membranes and Possible Signatures of Lost Momentum, Springer Proc. Phys. 137 (2011) 21 [arXiv:1007.4777] [INSPIRE].
  47. [47]
    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
  48. [48]
    I. Kirsch, Generalizations of the AdS/CFT correspondence, Fortsch. Phys. 52 (2004) 727 [hep-th/0406274] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    M. Araujo, D. Arean, J. Erdmenger and J.M. Lizana, Holographic charge localization at brane intersections, JHEP 08 (2015) 146 [arXiv:1505.05883] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  50. [50]
    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
  51. [51]
    I. Ya. Aref’eva, A.A. Slavnov and L.D. Faddeev, Generating functional for the S-matrix in gauge theories, Theor. Math. Phys. 21 (1974) 1165.Google Scholar
  52. [52]
    J. de Boer, M.M. Sheikh-Jabbari and J. Simon, Near Horizon Limits of Massless BTZ and Their CFT Duals, Class. Quant. Grav. 28 (2011) 175012 [arXiv:1011.1897] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    A.A. Bytsenko, L. Vanzo and S. Zerbini, Quantum correction to the entropy of the (2 + 1)-dimensional black hole, Phys. Rev. D 57 (1998) 4917 [gr-qc/9710106] [INSPIRE].ADSMathSciNetGoogle Scholar
  54. [54]
    V. Balasubramanian, A. Naqvi and J. Simon, A Multiboundary AdS orbifold and DLCQ holography: A Universal holographic description of extremal black hole horizons, JHEP 08 (2004) 023 [hep-th/0311237] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
  56. [56]
    D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
  57. [57]
    I. Ya. Aref’eva, M.A. Khramtsov and M.D. Tikhanovskaya, Holographic Dual to Conical Defects III: Improved Image Method, to appear.Google Scholar
  58. [58]
    V. Balasubramanian, P. Kraus and M. Shigemori, Massless black holes and black rings as effective geometries of the D1 − D5 system, Class. Quant. Grav. 22 (2005) 4803 [hep-th/0508110] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    S. Lin, Holographic thermalization with initial long range correlation, Phys. Rev. D 93 (2016) 026007 [arXiv:1511.07622] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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