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The AdS/CFT Correspondence

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Handbook of Quantum Gravity

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Abstract

A short introduction to the Anti-de-Sitter/Conformal Field Theory correspondence and related ideas.

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References

  1. J.M. Maldacena, Adv. Theor. Math. Phys. 2, 231–252 (1998). https://doi.org/10.1023/A:1026654312961, [ar**v:hep-th/9711200 [hep-th]]

  2. S.S. Gubser, I.R. Klebanov, A.M. Polyakov, Phys. Lett. B 428, 105–114 (1998). https://doi.org/10.1016/S0370-2693(98)00377-3, [ar**v:hep-th/9802109 [hep-th]]

  3. E. Witten, Adv. Theor. Math. Phys. 2, 253–291 (1998). https://doi.org/10.4310/ATMP.1998.v2.n2.a2, [ar**v:hep-th/9802150 [hep-th]]

  4. P. Breitenlohner, D.Z. Freedman, Phys. Lett. B 115, 197–201 (1982). https://doi.org/10.1016/0370-2693(82)90643-8

    Article  ADS  MathSciNet  Google Scholar 

  5. I.R. Klebanov, E. Witten, Nucl. Phys. B 556, 89–114 (1999). https://doi.org/10.1016/S0550-3213(99)00387-9, [ar**v:hep-th/9905104 [hep-th]]

  6. P.A.M. Dirac, J. Math. Phys. 4, 901–909 (1963). https://doi.org/10.1063/1.1704016

    Google Scholar 

  7. S.R. Coleman, F. De Luccia, Phys. Rev. D 21, 3305 (1980). https://doi.org/10.1103/PhysRevD.21.3305

    Article  ADS  MathSciNet  Google Scholar 

  8. H. Ooguri, C. Vafa, Adv. Theor. Math. Phys. 21, 1787–1801 (2017). https://doi.org/10.4310/ATMP.2017.v21.n7.a8, [ar**v:1610.01533 [hep-th]]

  9. J. Polchinski, String theory. Superstring Theory and Beyond, vol. 2 (Cambridge University Press, 2007). ISBN 978-0-511-25228-0, 978-0-521-63304-8, 978-0-521-67228-3. https://doi.org/10.1017/CBO9780511618123

  10. M. Henningson, K. Skenderis, JHEP 07, 023 (1998). https://doi.org/10.1088/1126-6708/1998/07/023, [ar**v:hep-th/9806087 [hep-th]]

    Article  ADS  Google Scholar 

  11. C. Fefferman, C.R. Graham, Elie Cartan et les Mathematiques d’ajourdhui (Asterique, 1985), p. 95

    Google Scholar 

  12. R. Emparan, C.V. Johnson, R.C. Myers, Phys. Rev. D 60, 104001 (1999). https://doi.org/10.1103/PhysRevD.60.104001, [ar**v:hep-th/9903238 [hep-th]]

    Article  ADS  MathSciNet  Google Scholar 

  13. V. Balasubramanian, P. Kraus, Commun. Math. Phys. 208, 413–428 (1999). https://doi.org/10.1007/s002200050764, [ar**v:hep-th/9902121 [hep-th]]

  14. S.W. Hawking, D.N. Page, Commun. Math. Phys. 87, 577 (1983). https://doi.org/10.1007/BF01208266

    Article  ADS  Google Scholar 

  15. E. Witten, Adv. Theor. Math. Phys. 2, 505–532 (1998). https://doi.org/10.4310/ATMP.1998.v2.n3.a3, [ar**v:hep-th/9803131 [hep-th]]

  16. M.R. Douglas, S.H. Shenker, Nucl. Phys. B 335, 635 (1990). https://doi.org/10.1016/0550-3213(90)90522-F

    Article  ADS  Google Scholar 

  17. D.J. Gross, A.A. Migdal, Phys. Rev. Lett. 64, 127 (1990). https://doi.org/10.1103/PhysRevLett.64.127

    Article  ADS  MathSciNet  Google Scholar 

  18. E. Brezin, V.A. Kazakov, Phys. Lett. B 236, 144–150 (1990). https://doi.org/10.1016/0370-2693(90)90818-Q

    Article  ADS  MathSciNet  Google Scholar 

  19. P. Saad, S.H. Shenker, D. Stanford, [ar**v:1903.11115 [hep-th]]

    Google Scholar 

  20. H. Osborn, A.C. Petkou, Ann. Phys. 231, 311–362 (1994). https://doi.org/10.1006/aphy.1994.1045, [ar**v:hep-th/9307010 [hep-th]]

  21. Z. Komargodski, A. Schwimmer, JHEP 12, 099 (2011). https://doi.org/10.1007/JHEP12(2011)099, [ar**v:1107.3987 [hep-th]]

    Article  ADS  Google Scholar 

  22. H. Casini, M. Huerta, Phys. Rev. D 85, 125016 (2012). https://doi.org/10.1103/PhysRevD.85.125016, [ar**v:1202.5650 [hep-th]]

    Article  ADS  Google Scholar 

  23. A. Strominger, C. Vafa, Phys. Lett. B 379, 99–104 (1996). https://doi.org/10.1016/0370-2693(96)00345-0, [ar**v:hep-th/9601029 [hep-th]]

  24. S.W. Hawking, Phys. Rev. D 14, 2460–2473 (1976). https://doi.org/10.1103/PhysRevD.14.2460

    Article  ADS  MathSciNet  Google Scholar 

  25. D.J. Gross, F. Wilczek, Phys. Rev. Lett. 30, 1343–1346 (1973). https://doi.org/10.1103/PhysRevLett.30.1343

    Article  ADS  Google Scholar 

  26. F. Gliozzi, J. Scherk, D.I. Olive, Nucl. Phys. B 122, 253–290 (1977). https://doi.org/10.1016/0550-3213(77)90206-1

    Article  ADS  Google Scholar 

  27. M.F. Sohnius, P.C. West, Phys. Lett. B 100, 245 (1981). https://doi.org/10.1016/0370-2693(81)90326-9

    Article  ADS  Google Scholar 

  28. G. ’t Hooft, Nucl. Phys. B 72, 461 (1974). https://doi.org/10.1016/0550-3213(74)90154-0

  29. A.M. Polyakov, Nucl. Phys. B Proc. Suppl. 68, 1–8 (1998). https://doi.org/10.1016/S0920-5632(98)00135-2, [ar**v:hep-th/9711002 [hep-th]]

  30. N. Beisert, C. Ahn, L.F. Alday, Z. Bajnok, J.M. Drummond, L. Freyhult, N. Gromov, R.A. Janik, V. Kazakov, T. Klose et al., Lett. Math. Phys. 99, 3–32 (2012). https://doi.org/10.1007/s11005-011-0529-2, [ar**v:1012.3982 [hep-th]]

  31. S. Caron-Huot, D. Mazac, L. Rastelli, D. Simmons-Duffin, JHEP 11, 164 (2021). https://doi.org/10.1007/JHEP11(2021)164, [ar**v:2106.10274 [hep-th]]

    Article  ADS  Google Scholar 

  32. D. Dorigoni, M.B. Green, C. Wen, JHEP 05, 089 (2021). https://doi.org/10.1007/JHEP05(2021)089, [ar**v:2102.09537 [hep-th]]

    Article  ADS  Google Scholar 

  33. S.M. Chester, M.B. Green, S.S. Pufu, Y. Wang, C. Wen, JHEP 11, 016 (2020). https://doi.org/10.1007/JHEP11(2020)016, [ar**v:1912.13365 [hep-th]]

    Article  ADS  Google Scholar 

  34. O. Aharony, O. Bergman, D.L. Jafferis, J. Maldacena, JHEP 10, 091 (2008). https://doi.org/10.1088/1126-6708/2008/10/091, [ar**v:0806.1218 [hep-th]]

    Article  ADS  Google Scholar 

  35. A. Kapustin, B. Willett, I. Yaakov, JHEP 03, 089 (2010). https://doi.org/10.1007/JHEP03(2010)089, [ar**v:0909.4559 [hep-th]]

    Article  ADS  Google Scholar 

  36. N. Drukker, M. Marino, P. Putrov, Commun. Math. Phys. 306, 511–563 (2011). https://doi.org/10.1007/s00220-011-1253-6, [ar**v:1007.3837 [hep-th]]

  37. J. Polchinski, Phys. Rev. Lett. 75, 4724–4727 (1995). https://doi.org/10.1103/PhysRevLett.75.4724, [ar**v:hep-th/9510017 [hep-th]]

  38. G.T. Horowitz, A. Strominger, Nucl. Phys. B 360, 197–209 (1991). https://doi.org/10.1016/0550-3213(91)90440-9

    Article  ADS  Google Scholar 

  39. J.D. Bekenstein, Phys. Rev. D 7, 2333–2346 (1973). https://doi.org/10.1103/PhysRevD.7.2333

    Article  ADS  MathSciNet  Google Scholar 

  40. G. ’t Hooft, Conf. Proc. C 930308, 284–296 (1993). [ar**v:gr-qc/9310026 [gr-qc]]

    Google Scholar 

  41. L. Susskind, J. Math. Phys. 36, 6377–6396 (1995). https://doi.org/10.1063/1.531249, [ar**v:hep-th/9409089 [hep-th]]

  42. N. Seiberg, Nucl. Phys. B 435, 129–146 (1995). https://doi.org/10.1016/0550-3213(94)00023-8, [ar**v:hep-th/9411149 [hep-th]]

  43. I.R. Klebanov, A.M. Polyakov, Phys. Lett. B 550, 213–219 (2002). https://doi.org/10.1016/S0370-2693(02)02980-5, [ar**v:hep-th/0210114 [hep-th]]

  44. M.A. Vasiliev, https://doi.org/10.1142/9789812793850_0030, [ar**v:hep-th/9910096 [hep-th]]

  45. S. Sachdev, J. Ye, Phys. Rev. Lett. 70, 3339 (1993). https://doi.org/10.1103/PhysRevLett.70.3339, [ar**v:cond-mat/9212030 [cond-mat]]; A. Kitaev, A simple model of quantum holography. http://online.kitp.ucsb.edu/online/entangled15/kitaev/. Talks at KITP, April 7, 2015

  46. J. Polchinski, M.J. Strassler, [ar**v:hep-th/0003136 [hep-th]]

    Google Scholar 

  47. N. Itzhaki, J.M. Maldacena, J. Sonnenschein, S. Yankielowicz, Phys. Rev. D 58, 046004 (1998). https://doi.org/10.1103/PhysRevD.58.046004, [ar**v:hep-th/9802042 [hep-th]]

    Article  ADS  MathSciNet  Google Scholar 

  48. G.J. Galloway, K. Schleich, D. Witt, E. Woolgar, Phys. Lett. B 505, 255–262 (2001). https://doi.org/10.1016/S0370-2693(01)00335-5, [ar**v:hep-th/9912119 [hep-th]]

  49. S.H. Shenker, D. Stanford, JHEP 12, 046 (2014). https://doi.org/10.1007/JHEP12(2014)046, [ar**v:1312.3296 [hep-th]]

    Article  ADS  Google Scholar 

  50. P. Gao, D.L. Jafferis, A.C. Wall, JHEP 12, 151 (2017). https://doi.org/10.1007/JHEP12(2017)151, [ar**v:1608.05687 [hep-th]]

    Article  ADS  Google Scholar 

  51. J.M. Maldacena, JHEP 04, 021 (2003). https://doi.org/0.1088/1126-6708/2003/04/021, [ar**v:hep-th/0106112 [hep-th]]

    Article  ADS  Google Scholar 

  52. S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006). https://doi.org/10.1103/PhysRevLett.96.181602, [ar**v:hep-th/0603001 [hep-th]]

    Article  ADS  MathSciNet  Google Scholar 

  53. V.E. Hubeny, M. Rangamani, T. Takayanagi, JHEP 07, 062 (2007). https://doi.org/10.1088/1126-6708/2007/07/062, [ar**v:0705.0016 [hep-th]]

    Article  ADS  Google Scholar 

  54. T. Faulkner, A. Lewkowycz, J. Maldacena, JHEP 11, 074 (2013). https://doi.org/10.1007/JHEP11(2013)074, [ar**v:1307.2892 [hep-th]]

    Article  ADS  Google Scholar 

  55. N. Engelhardt, A.C. Wall, JHEP 01, 073 (2015). https://doi.org/10.1007/JHEP01(2015)073, [ar**v:1408.3203 [hep-th]]

    Article  ADS  Google Scholar 

  56. J. Maldacena, L. Susskind, Fortsch. Phys. 61, 781–811 (2013). https://doi.org/10.1002/prop.201300020, [ar**v:1306.0533 [hep-th]]

  57. B. Czech, J.L. Karczmarek, F. Nogueira, M. Van Raamsdonk, Class. Quant. Grav. 29, 155009 (2012). https://doi.org/10.1088/0264-9381/29/15/155009, [ar**v:1204.1330 [hep-th]]

    Article  ADS  Google Scholar 

  58. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, A. Tajdini, Rev. Mod. Phys. 93(3), 035002 (2021). https://doi.org/10.1103/RevModPhys.93.035002, [ar**v:2006.06872 [hep-th]]

  59. B. Swingle, Phys. Rev. D 86, 065007 (2012). https://doi.org/10.1103/PhysRevD.86.065007, [ar**v:0905.1317 [cond-mat.str-el]]

    Article  ADS  Google Scholar 

  60. A. Almheiri, X. Dong, D. Harlow, JHEP 04, 163 (2015). https://doi.org/10.1007/JHEP04(2015)163, [ar**v:1411.7041 [hep-th]]

    Article  ADS  Google Scholar 

  61. T. Banks, W. Fischler, S.H. Shenker, L. Susskind, Phys. Rev. D 55, 5112–5128 (1997). https://doi.org/10.1103/PhysRevD.55.5112, [ar**v:hep-th/9610043 [hep-th]]

  62. E. Witten, [ar**v:hep-th/0106109 [hep-th]]

    Google Scholar 

  63. A. Strominger, JHEP 10, 034 (2001). https://doi.org/10.1088/1126-6708/2001/10/034, [ar**v:hep-th/0106113 [hep-th]]

    Article  ADS  Google Scholar 

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Acknowledgements

This field was developed by numerous authors over many years, and we could not do justice to all their contributions. There exist other reviews and books that cover the subject more extensively and include applications to other fields beyond problems in quantum gravity.

J.M. is supported in part by U.S. Department of Energy grant DE-SC0009988 and by the Simons Foundation grant 385600.

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, NJ, USA

    Juan Maldacena

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  1. Juan Maldacena
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Correspondence to Juan Maldacena .

Editor information

Editors and Affiliations

  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Department of Physics, Southern University of Science and Techn, Shenzhen, China

    Leonardo Modesto

  3. Departamento de Física, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brazil

    Ilya Shapiro

Section Editor information

  1. Turin University, Turin, Italy

    Carlo Angelantonj

  2. Sorbonne Universit´e, Paris, France

    Ignatios Antoniadis

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Maldacena, J. (2024). The AdS/CFT Correspondence. In: Bambi, C., Modesto, L., Shapiro, I. (eds) Handbook of Quantum Gravity. Springer, Singapore. https://doi.org/10.1007/978-981-19-3079-9_65-1

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  • DOI: https://doi.org/10.1007/978-981-19-3079-9_65-1

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