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Pedagogical introduction to the Sachdev—Ye—Kitaev model and two-dimensional dilaton gravity

 a, b
a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
b National Research Center "Kurchatov Institute", Alikhanov Institute of Theoretical and Experimental Physics, ul. B. Cheremushkinskaya 25, Moscow, 117218, Russian Federation

The Sachdev—Ye—Kitaev model and two-dimensional dilaton gravity have recently been attracting increasing attention of the high-energy and condensed-matter physics communities. The success of these models is due to their remarkable properties. Following the original papers, we broadly discuss the properties of these models, including the diagram technique in the limit of a large number of degrees of freedom, the emergence of conformal symmetry in the infrared limit, effective action, four-point functions, and chaos. We also briefly discuss some recent results in this field. On the one hand, we attempt to be maximally rigorous, which means considering all the details and gaps in the argument; on the other hand, we believe that this review can be suitable for those who are not familiar with the relevant models.

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Fulltext is also available at DOI: 10.3367/UFNe.2020.06.038805
Keywords: Sachdev—Ye—Kitaev model, two-dimensional gravity, quantum chaos, 1/N expansion, AdS/CFT correspondence
PACS: 03.70.+k, 04.62.+v, 04.70.Dy, 05.30.Fk, 05.45.Ac, 05.45.Mt, 11.10.Kk, 11.10.Wx (all)
DOI: 10.3367/UFNe.2020.06.038805
URL: https://ufn.ru/en/articles/2021/3/a/
000656123500001
2-s2.0-85108009429
2021PhyU...64..219T
Citation: Trunin D A "Pedagogical introduction to the Sachdev—Ye—Kitaev model and two-dimensional dilaton gravity" Phys. Usp. 64 219–252 (2021)
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Received: 3rd, March 2020, revised: 28th, June 2020, 29th, June 2020

Оригинал: Трунин Д А «Педагогическое введение в модель Сачдева—Йе—Китаева и двумерную дилатонную гравитацию» УФН 191 225–261 (2021); DOI: 10.3367/UFNr.2020.06.038805

References (175) ↓ Cited by (31) Similar articles (20)

  1. Kitaev A "Hidden correlations in the Hawking radiation and thermal noise" Fundamental Physics Prize Symp., November 10, 2014; https://www.youtube.com/embed/OQ9qN8j7EZI; Kitaev A ""A simple model of quantum holography, Pt. 1" Kavli Institute for Theoretical Physics, Univ. of California, Santa Barbara, CA, USA, April 7, 2015; https://online.kitp.ucsb.edu/online/entangled15/kitaev/; Kitaev A ""A simple model of quantum holography, Pt. 2" Kavli Institute for Theoretical Physics, Univ. of California, Santa Barbara, CA, USA, April 7, 2015; https://online.kitp.ucsb.edu/online/entangled15/kitaev2/
  2. Sachdev S, Ye J Phys. Rev. Lett. 70 3339 (1993); Sachdev S, Ye J cond-mat/9212030
  3. Sachdev S Phys. Rev. Lett. 105 151602 (2010); Sachdev S arXiv:1006.3794
  4. Polchinski J, Rosenhaus V J. High Energ. Phys. 2016 1 (2016); Polchinski J, Rosenhaus V arXiv:1601.06768
  5. Maldacena J, Stanford D Phys. Rev. D 94 106002 (2016); Maldacena J, Stanford D arXiv:1604.07818
  6. Kitaev A, Suh S J J. High Energ. Phys. 2018 183 (2018); Kitaev A, Suh S J arXiv:1711.08467
  7. Jevicki A, Suzuki K, Yoon J J. High Energ. Phys. 2016 7 (2016); Jevicki A, Suzuki K, Yoon J arXiv:1603.06246
  8. Jevicki A, Suzuki K J. High Energ. Phys. 2016 046 (2016); Jevicki A, Suzuki K arXiv:1608.07567
  9. Maldacena J, Shenker S H, Stanford D J. High Energ. Phys. 2016 106 (2016); Maldacena J, Shenker S H, Stanford D arXiv:1503.01409
  10. Maldacena J, Stanford D, Yang Z Prog. Theor. Exp. Phys. 104 (2016); Maldacena J, Stanford D, Yang Z arXiv:1606.01857
  11. Jensen K Phys. Rev. Lett. 117 111601 (2016); Jensen K arXiv:1605.06098
  12. Almheiri A, Polchinski J J. High Energ. Phys. 2015 14 (2015); Almheiri A, Polchinski J arXiv:1402.6334
  13. Engelsöy J, Mertens T G, Verlinde H J. High Energ. Phys. 2016 139 (2016); Engelsöy J, Mertens T G, Verlinde H arXiv:1606.03438
  14. Sekino Y, Susskind L J. High Energ. Phys. 2008 (10) 065 (2008); Sekino Y, Susskind L arXiv:0808.2096
  15. Susskind L arXiv:1101.6048
  16. Lashkari N et al J. High Energ. Phys. 2013 22 (2013); Lashkari N et al arXiv:1101.6048
  17. Maldacena J, Stanford D, Yang Z Fortschr. Phys. 65 1700034 (2017); Maldacena J, Stanford D, Yang Z arXiv:1704.05333
  18. Maldacena J, Qi X-L arXiv:1804.00491
  19. Maldacena J, Milekhin A, Popov F arXiv:1807.04726
  20. Maldacena J, Milekhin A arXiv:1912.03276
  21. Hartnoll S A, Lucas A, Sachdev S arXiv:1612.07324
  22. Song X-Y, Jian C-M, Balents L Phys. Rev. Lett. 119 216601 (2017); Song X-Y, Jian C-M, Balents L arXiv:1705.00117
  23. Sachdev S Phys. Rev. X 5 041025 (2015); Sachdev S arXiv:1506.05111
  24. Larkin A I, Ovchinnikov Yu N Zh. Eksp. Teor. Fiz. 55 2262 (1968); Larkin A I, Ovchinnikov Yu N Sov. Phys. JETP 28 1200 (1969)
  25. Almheiri A et al J. High Energ. Phys. 2013 18 (2013); Almheiri A et al arXiv:1304.6483
  26. Shenker S H, Stanford D J. High Energ. Phys. 2014 67 (2014); Shenker S H, Stanford D arXiv:1306.0622
  27. Gur-Ari G, Hanada M, Shenker S H J. High Energ. Phys. 2016 91 (2016); Gur-Ari G, Hanada M, Shenker S H arXiv:1512.00019
  28. Eichhorn R, Linz S J, Hänggi P Chaos Solitons Fractals 12 1377 (2001)
  29. de Wijn A S, Hess B, Fine B V Phys. Rev. Lett. 109 034101 (2012); de Wijn A S, Hess B, Fine B V arXiv:1205.2901
  30. Fine B V et al Phys. Rev. E 89 012923 (2014); Fine B V et al arXiv:1305.2817
  31. Aleiner I L, Larkin A I Phys. Rev. B 54 14423 (1996); Aleiner I L, Larkin A I cond-mat/9603121
  32. Silvestrov P G, Beenakker C W J Phys. Rev. E 65 035208(R) (2002); Silvestrov P G, Beenakker C W J nlin/0111042
  33. Berman G P, Zaslavsky G M Physica A 91 450 (1978)
  34. Zaslavsky G M Phys. Rep. 80 157 (1981)
  35. Roberts D A, Stanford D Phys. Rev. Lett. 115 131603 (2015); Roberts D A, Stanford D arXiv:1412.5123
  36. Romero-Bermúdez A, Schalm K, Scopelliti V J. High Energ. Phys. 2019 107 (2019); Romero-Bermúdez A, Schalm K, Scopelliti V arXiv:1903.09595
  37. Polyakov A M Gauge Fields And Strings (Chur: Harwood Acad. Publ., 1987); Per. na russk. yaz., Polyakov A M Kalibrovochnye Polya i Struny (Izhevsk: Udmurtskii universitet, 1999)
  38. Makeenko Y M-Theory And Quantum Geometry (NATO Science Ser. C) Vol. 556 (Eds L Thorlacius, T Jonsson) (Dordrecht: Kluwer Acad. Publ., 2000) p. 285; Makeenko Y hep-th/0001047
  39. Cotler J S, Ding D, Penington G R Ann. Physics 396 318 (2018); Cotler J S, Ding D, Penington G R arXiv:1704.02979
  40. Xu T, Scaffidi T, Cao X Phys. Rev. Lett. 124 140602 (2020); Xu T, Scaffidi T, Cao X arXiv:1912.11063
  41. Hashimoto K, Murata K, Yoshii R J. High Energ. Phys. 2017 138 (2017); Hashimoto K, Murata K, Yoshii R arXiv:1703.09435
  42. Gharibyan H et al J. High Energ. Phys. 2018 124 (2018); Gharibyan H et al arXiv:1803.08050; Gharibyan H et al J. High Energ. Phys. 2019 197 (2019), Erratum
  43. Haake F Quantum Signatures Of Chaos (Berlin: Springer, 2010)
  44. Ott E Chaos In Dynamical Systems (Cambridge: Cambridge Univ. Press, 2012)
  45. Stöckmann H-J Quantum Chaos: An Introduction (Cambridge: Cambridge Univ. Press, 1999)
  46. Srednicki M Phys. Rev. E 50 888 (1994); Srednicki M cond-mat/9403051
  47. Deutsch J M Rep. Prog. Phys. 81 082001 (2018); Deutsch J M arXiv:1805.01616
  48. D’Alessio L et al Adv. Phys. 65 239 (2016); D’Alessio L et al arXiv:1509.06411
  49. Foini L, Kurchan J Phys. Rev. E 99 042139 (2019); Foini L, Kurchan J arXiv:1803.10658
  50. Murthy C, Srednicki M Phys. Rev. Lett. 123 230606 (2019); Murthy C, Srednicki M arXiv:1906.10808
  51. Parker D E et al Phys. Rev. X 9 041017 (2019); Parker D E et al arXiv:1812.08657
  52. Avdoshkin A, Dymarsky A Phys. Rev. Res. 2 043234 (2020); Avdoshkin A, Dymarsky A arXiv:1911.09672
  53. Huang Y, Brandão F G S L, Zhang Y-L Phys. Rev. Lett. 123 010601 (2019); Huang Y, Brandão F G S L, Zhang Y-L arXiv:1705.07597
  54. Sonner J, Vielma M J. High Energ. Phys. 2017 (11) 149 (2017); Sonner J, Vielma M arXiv:1707.08013
  55. Nayak P, Sonner J, Vielma M J. High Energ. Phys. 2019 (10) 19 (2019); Nayak P, Sonner J, Vielma M arXiv:1903.00478
  56. Anous T, Sonner J SciPost Phys. 7 003 (2019); Anous T, Sonner J arXiv:1903.03143
  57. Page D N Phys. Rev. Lett. 71 1291 (1993); Page D N gr-qc/9305007
  58. Nishioka T, Ryu S, Takayanagi T J. Phys. A 42 504008 (2009); Nishioka T, Ryu S, Takayanagi T arXiv:0905.0932
  59. Anninos D, Galante D A, Hofman D M J. High Energ. Phys. 2019 (07) 38 (2019); Anninos D, Galante D A, Hofman D M arXiv:1811.08153
  60. Aalsma L, Shiu G J. High Energ. Phys. 2020 (05) 152 (2020); Aalsma L, Shiu G arXiv:2002.01326
  61. Hayden P, Preskill J J. High Energ. Phys. 2007 (09) 120 (2007); Hayden P, Preskill J arXiv:0708.4025
  62. Almheiri A et al J. High Energ. Phys. 2013 (02) 62 (2013); Almheiri A et al arXiv:1207.3123
  63. Mathur S D Class. Quantum Grav. 26 224001 (2009); Mathur S D arXiv:0909.1038
  64. Roberts D A, Stanford D, Streicher A J. High Energ. Phys. 2018 (06) 122 (2018); Roberts D A, Stanford D, Streicher A arXiv:1802.02633
  65. Qi X-L, Streicher A J. High Energ. Phys. 2019 (08) 12 (2019); Qi X-L, Streicher A arXiv:1810.11958
  66. Hartman T, Maldacena J J. High Energ. Phys. 2013 (05) 14 (2013); Hartman T, Maldacena J arXiv:1303.1080
  67. Asplund C T et al J. High Energ. Phys. 2015 (09) 110 (2015); Asplund C T et al arXiv:1506.03772
  68. Aref’eva I Ya, Khramtsov M A, Tikhanovskaya M D J. High Energ. Phys. 2017 (09) 115 (2017); Aref’eva I Ya, Khramtsov M A, Tikhanovskaya M D arXiv:1706.07390
  69. Camanho X O et al J. High Energ. Phys. 2016 (02) 20 (2016); Camanho X O et al arXiv:1407.5597
  70. Roberts D A, Swingle B Phys. Rev. Lett. 117 091602 (2016); Roberts D A, Swingle B arXiv:1603.09298
  71. Hosur P et al J. High Energ. Phys. 2016 (02) 4 (2016); Hosur P et al arXiv:1511.04021
  72. Nahum A, Vijay S, Haah J Phys. Rev. X 8 021014 (2018); Nahum A, Vijay S, Haah J arXiv:1705.08975
  73. Mezei M, Stanford D J. High Energ. Phys. 2017 (05) 65 (2017); Mezei M, Stanford D arXiv:1608.05101
  74. Roberts D A, Stanford D, Susskind L J. High Energ. Phys. 2015 (03) 51 (2015); Roberts D A, Stanford D, Susskind L arXiv:1409.8180
  75. Shenker S H, Stanford D J. High Energ. Phys. 2014 (12) 46 (2014); Shenker S H, Stanford D arXiv:1412.6087
  76. Shenker S H, Stanford D J. High Energ. Phys. 2015 (05) 132 (2015); Shenker S H, Stanford D arXiv:1412.6087
  77. Turiaci G J, Verlinde H J. High Energ. Phys. 2016 (12) 110 (2016); Turiaci G J, Verlinde H arXiv:1603.03020
  78. Fitzpatrick A L, Kaplan J J. High Energ. Phys. 2016 (05) 70 (2016); Fitzpatrick A L, Kaplan J arXiv:1601.06164
  79. Murugan J, Stanford D, Witten E J. High Energ. Phys. 2017 (08) 146 (2017); Murugan J, Stanford D, Witten E arXiv:1706.05362
  80. Fu W et al Phys. Rev. D 95 026009 (2017); Fu W et al Phys. Rev. D 95 069904 (2017), Erratum; Fu W et al arXiv:1610.08917
  81. Gross D J, Rosenhaus V J. High Energ. Phys. 2017 (02) 93 (2017); Gross D J, Rosenhaus V arXiv:1610.01569
  82. Gu Y, Qi X-L, Stanford D J. High Energ. Phys. 2017 (05) 125 (2017); Gu Y, Qi X-L, Stanford D arXiv:1609.07832
  83. Stanford D J. High Energ. Phys. 2016 (10) 9 (2016); Stanford D arXiv:1512.07687
  84. Aleiner I L, Faoro L, Ioffe L B Ann. Physics 375 378 (2016); Aleiner I L, Faoro L, Ioffe L B arXiv:1609.01251
  85. Yao N Y et al arXiv:1607.01801
  86. Huang Y, Zhang Y-L, Chen X Ann. Physik 529 1600318 (2017); Huang Y, Zhang Y-L, Chen X arXiv:1608.01091
  87. Swingle B, Chowdhury D Phys. Rev. B 95 060201(R) (2017); Swingle B, Chowdhury D arXiv:1608.03280
  88. Shen H et al Phys. Rev. B 96 054503 (2017); Shen H et al arXiv:1608.02438
  89. Dóra B, Moessner R Phys. Rev. Lett. 119 026802 (2017); Dóra B, Moessner R arXiv:1612.00614
  90. Bohrdt A et al New J. Phys. 19 063001 (2017); Bohrdt A et al arXiv:1612.02434
  91. Patel A A, Sachdev S Proc. Natl. Acad. Sci. USA 114 1844 (2017); Patel A A, Sachdev S arXiv:1611.00003
  92. Patel A A et al Phys. Rev. X 7 031047 (2017); Patel A A et al arXiv:1703.07353
  93. Lin C-J, Motrunich O I Phys. Rev. B 97 144304 (2018); Lin C-J, Motrunich O I arXiv:1801.01636
  94. von Keyserlingk C W et al Phys. Rev. X 8 021013 (2018); von Keyserlingk C W et al arXiv:1705.08910
  95. Arseev P I Usp. Fiz. Nauk 185 1271 (2015); Arseev P I Phys. Usp. 58 1159 (2015)
  96. Kamenev A Field Theory Of Non-Equilibrium Systems (Cambridge: Cambridge Univ. Press, 2011); Kamenev A cond-mat/0412296
  97. Krotov D, Polyakov A M Nucl. Phys. B 849 410 (2011); Krotov D, Polyakov A M arXiv:1012.2107
  98. Akhmedov E T Int. J. Mod. Phys. D 23 1430001 (2014); Akhmedov E T arXiv:1309.2557
  99. Akhmedov E T, Godazgar H, Popov F K Phys. Rev. D 93 024029 (2016); Akhmedov E T, Godazgar H, Popov F K arXiv:1508.07500
  100. Akhmedov E T et al Phys. Rev. D 96 025002 (2017); Akhmedov E T et al arXiv:1701.07226
  101. Akhmedov E T, Moschella U, Popov F K Phys. Rev. D 99 086009 (2019); Akhmedov E T, Moschella U, Popov F K arXiv::1901.07293
  102. Haehl F M et al SciPost Phys. 6 001 (2019); Haehl F M et al arXiv:1701.02820
  103. Sárosi G PoS Modave2017 001 (2018); Sárosi G arXiv:1711.08482
  104. Rosenhaus V J. Phys. A 52 323001 (2019); Rosenhaus V arXiv:1807.03334
  105. Krajewski T et al Phys. Rev. D 99 126014 (2019); Krajewski T et al arXiv:1812.03008
  106. Witten E J. Phys. A 52 474002 (2019); Witten E arXiv:1610.09758
  107. Gurau R Nucl. Phys. B 916 386 (2017); Gurau R arXiv:1611.04032
  108. Klebanov I R, Tarnopolsky G Phys. Rev. D 95 046004 (2017); Klebanov I R, Tarnopolsky G arXiv:1611.08915
  109. Klebanov I R, Popov F, Tarnopolsky G PoS TASI2017 004 (2018); Klebanov I R, Popov F, Tarnopolsky G arXiv:1808.09434
  110. Klebanov I R, Pallegar P N, Popov F K Phys. Rev. D 100 086003 (2019); Klebanov I R, Pallegar P N, Popov F K arXiv:1905.06264
  111. Nishinaka T, Terashima S Nucl. Phys. B 926 321 (2018); Nishinaka T, Terashima S arXiv:1611.10290
  112. Peskin M E, Schroeder D V An Introduction To Quantum Field Theory (Reading, Mass.: Addison-Wesley Publ. Co., 1995); Per. na russk. yaz., Peskin M, Shreder D Vvedenie v Kvantovuyu Teoriyu Polya (Izhevsk: RKhD, 2001)
  113. Bonzom V, Nador V, Tanasa A Lett. Math. Phys. 109 2611 (2019); Bonzom V, Nador V, Tanasa A arXiv:1808.10314
  114. Gurau R Europhys. Lett. 119 30003 (2017); Gurau R arXiv:1702.04228
  115. Parcollet O, Georges A Phys. Rev. B 59 5341 (1999); Parcollet O, Georges A cond-mat/9806119
  116. Lunkin A V, Tikhonov K S, Feigel’man M V Phys. Rev. Lett. 121 236601 (2018); Lunkin A V, Tikhonov K S, Feigel’man M V arXiv:1806.11211
  117. Bagrets D, Altland A, Kamenev A Nucl. Phys. B 911 191 (2016); Bagrets D, Altland A, Kamenev A arXiv:1607.00694
  118. Aref’eva I et al J. High Energ. Phys. 2019 (07) 113 (2019); Aref’eva I et al arXiv:1811.04831
  119. Wang H et al J. High Energ. Phys. 2019 (09) 57 (2019); Wang H et al arXiv:1812.02666
  120. Cotler J S et al J. High Energ. Phys. 2017 (05) 118 (2017); Cotler J S et al J. High Energ. Phys. 2018 (09) 2 (2018), Erratum; Cotler J S et al arXiv:1611.04650
  121. Kitaev A arXiv:1711.08169
  122. Gross D J, Rosenhaus V J. High Energ. Phys. 2017 (12) 148 (2017); Gross D J, Rosenhaus V arXiv:1710.08113
  123. Gross D J, Rosenhaus V J. High Energ. Phys. 2017 (05) 92 (2017); Gross D J, Rosenhaus V arXiv:1702.08016
  124. Reed M, Simon B Methods Of Modern Mathematical Physics Vol. 1 Functional Analysis (New York: Academic Press, 1980)
  125. Gradshtein I S, Ryzhik I M Tablitsy Integralov, Ryadov i Proizvedenii (SPb.: BKhV-Peterburg, 2011); Per. na angl. yaz., Gradshteyn I S, Ryzhik I M Tables Of Integrals, Series, And Products (San Diego, CA: Associated Press, 2007)
  126. Bagrets D, Altland A, Kamenev A Nucl. Phys. B 921 727 (2017); Bagrets D, Altland A, Kamenev A arXiv:1702.08902
  127. Streicher A J. High Energ. Phys. 2020 (02) 48 (2020); Streicher A arXiv:1911.10171
  128. Choi C, Mezei M, Sárosi G CERN-TH-2019-206 (Geneva: CERN, 2019); Choi C, Mezei M, Sárosi G arXiv:1912.00004
  129. Thomi P, Isaak B, Hajicek P Phys. Rev. D 30 1168 (1984)
  130. Nayak P et al J. High Energ. Phys. 2018 (09) 48 (2018); Nayak P et al arXiv:1802.09547
  131. Grumiller D, Kummer W, Vassilevich D V Phys. Rep. 369 327 (2002); Grumiller D, Kummer W, Vassilevich D V hep-th/0204253
  132. Jackiw R Nucl. Phys. B 252 343 (1985)
  133. Teitelboim C Phys. Lett. B 126 41 (1983)
  134. Kolekar K S, Narayan K Phys. Rev. D 98 046012 (2018); Kolekar K S, Narayan K arXiv:1803.06827
  135. Akhmedov E T, Moschella U, Popov F K J. High Energ. Phys. 2018 (03) 183 (2018); Akhmedov E T, Moschella U, Popov F K arXiv:1802.02955
  136. Spradlin M, Strominger A J. High Energ. Phys. 1999 (11) 021 (1999); Spradlin M, Strominger A hep-th/9904143
  137. Akhmedov E T Phys. Lett. B 442 152 (1998); Akhmedov E T hep-th/9806217
  138. de Boer J, Verlinde E P, Verlinde H L J. High Energ. Phys. 2000 (08) 003 (2000); de Boer J, Verlinde E P, Verlinde H L hep-th/9912012
  139. Skenderis K Class. Quantum Grav. 19 5849 (2002); Skenderis K hep-th/0209067
  140. Grumiller D, McNees R J. High Energ. Phys. 2007 (04) 074 (2007); Grumiller D, McNees R hep-th/0703230
  141. Grumiller D et al J. High Energ. Phys. 2017 (10) 203 (2017); Grumiller D et al arXiv:1708.08471
  142. Cvetič M, Papadimitriou I J. High Energ. Phys. 2016 (12) 008 (2016); Cvetič M, Papadimitriou I J. High Energ. Phys. 2017 (01) 120 (2017)
  143. Davis J L, McNees R J. High Energ. Phys. 2005 (09) 072 (2005); Davis J L, McNees R hep-th/0411121
  144. González H A, Grumiller D, Salzer J J. High Energ. Phys. 2018 (05) 83 (2018); González H A, Grumiller D, Salzer J arXiv:1802.01562
  145. Grumiller D, Leston M, Vassilevich D Phys. Rev. D 89 044001 (2014); Grumiller D, Leston M, Vassilevich D arXiv:1311.7413
  146. Grumiller D, Salzer J, Vassilevich D J. High Energ. Phys. 2015 (12) 015 (2015); Grumiller D, Salzer J, Vassilevich D arXiv:1509.08486
  147. Maldacena J Int. J. Theor. Phys. 38 1113 (1999); Maldacena J Adv. Theor. Math. Phys. 2 231 (1998); Maldacena J hep-th/9711200
  148. Gubser S S, Klebanov I R, Polyakov A M Phys. Lett. B 428 105 (1998); Gubser S S, Klebanov I R, Polyakov A M hep-th/9802109
  149. Aharony O et al Phys. Rep. 323 183 (2000); Aharony O et al hep-th/9905111
  150. Witten E Adv. Theor. Math. Phys. 2 253 (1998); Witten E hep-th/9802150
  151. Freedman D Z et al Nucl. Phys. B 546 96 (1999); Freedman D Z et al hep-th/9804058
  152. Krishnan C, Sanyal S, Bala Subramanian.P N J. High Energ. Phys. 2017 (03) 56 (2017); Krishnan C, Sanyal S, Bala Subramanian P N arXiv:1612.06330
  153. Bonzom V, Lionni L, Tanasa A J. Math. Phys. 58 052301 (2017); Bonzom V, Lionni L, Tanasa A arXiv:1702.06944
  154. Choudhury S et al J. High Energ. Phys. 2018 (06) 94 (2018); Choudhury S et al arXiv:1707.09352
  155. Bulycheva K et al Phys. Rev. D 97 026016 (2018); Bulycheva K et al arXiv:1707.09347
  156. Klebanov I R et al Phys. Rev. D 97 106023 (2018); Klebanov I R et al arXiv:1802.10263
  157. Giombi S et al Phys. Rev. D 98 105005 (2018); Giombi S et al arXiv:1808.04344
  158. Pakrouski K et al Phys. Rev. Lett. 122 011601 (2019); Pakrouski K et al arXiv:1808.07455
  159. Popov F K Phys. Rev. D 101 026020 (2020); Popov F K arXiv:1907.02440
  160. Gaitan G et al Phys. Rev. D 101 126002 (2020); Gaitan G et al arXiv:2002.02066
  161. Ferrari F Ann. Inst. Henri Poincaré 6 427 (2019); Ferrari F arXiv:1701.01171
  162. Azeyanagi T et al Ann. Physics 393 308 (2018); Azeyanagi T et al arXiv:1710.07263
  163. Ferrari F, Rivasseau V, Valette G Commun. Math. Phys. 370 403 (2019); Ferrari F, Rivasseau V, Valette G arXiv:1709.07366
  164. Azeyanagi T, Ferrari F, Schaposnik Massolo F I Phys. Rev. Lett. 120 061602 (2018); Azeyanagi T, Ferrari F, Schaposnik Massolo F I arXiv:1707.03431
  165. Gu Y et al J. High Energ. Phys. 2020 (02) 157 (2020); Gu Y et al arXiv:1910.14099
  166. Bulycheva K J. High Energ. Phys. 2017 (12) 69 (2017); Bulycheva K arXiv:1706.07411
  167. Davison R A et al Phys. Rev. B 95 155131 (2017); Davison R A et al arXiv:1612.00849
  168. Maldacena J J. High Energ. Phys. 2003 (04) 021 (2003); Maldacena J hep-th/0106112
  169. Cornalba L et al J. High Energ. Phys. 2007 (08) 019 (2007); Cornalba L et al hep-th/0611122
  170. Grozdanov S, Schalm K, Scopelliti V Phys. Rev. E 99 012206 (2019); Grozdanov S, Schalm K, Scopelliti V arXiv:1804.09182
  171. Kitaev A Yu Usp. Fiz. Nauk 171 (Suppl. 10) 131 (2001); Kitaev A Yu Phys. Usp. 44 (10S) 131 (2001); Kitaev A Yu cond-mat/0010440
  172. Kourkoulou I, Maldacena J arXiv:1707.02325
  173. García-García A M, Verbaarschot J J M Phys. Rev. D 94 126010 (2016); García-García, Verbaarschot J J M arXiv:1610.03816
  174. Evans T S, Steer D A Nucl. Phys. B 474 481 (1996); Evans T S, Steer D A hep-ph/9601268
  175. Trunin D A Int. J. Mod. Phys. A 33 1850140 (2018); Trunin D A arXiv:1805.04856
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