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Journal of High Energy Physics

, 2018:101 | Cite as

A note on the complex SYK model and warped CFTs

  • Pankaj Chaturvedi
  • Yingfei GuEmail author
  • Wei Song
  • Boyang Yu
Open Access
Regular Article - Theoretical Physics

Abstract

We discuss the connections between the complex SYK model at the conformal limit and warped conformal field theories. Both theories have an SL(2, ℝ) × U(1) global symmetry. We present comparisons on symmetries, correlation functions, the effective action and the entropy formula. We also use modular covariance to reinterpret results in the complex SYK model.

Keywords

AdS-CFT Correspondence Conformal Field Theory Holography and condensed matter physics (AdS/CMT) Models of Quantum Gravity 

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.

References

  1. [1]
    J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
  3. [3]
    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].
  4. [4]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
  6. [6]
    I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Cargese Lectures on the Kerr/CFT Correspondence, Nucl. Phys. Proc. Suppl. 216 (2011) 194 [arXiv:1103.2355] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    G. Compère, The Kerr/CFT correspondence and its extensions, Living Rev. Rel. 15 (2012) 11 [arXiv:1203.3561] [INSPIRE].CrossRefzbMATHGoogle Scholar
  8. [8]
    J.M. Bardeen and G.T. Horowitz, The Extreme Kerr throat geometry: A Vacuum analog of AdS 2 × S 2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [INSPIRE].
  9. [9]
    G. Compère, M. Guica and M.J. Rodriguez, Two Virasoro symmetries in stringy warped AdS 3, JHEP 12 (2014) 012 [arXiv:1407.7871] [INSPIRE].
  10. [10]
    S. Detournay, T. Hartman and D.M. Hofman, Warped Conformal Field Theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
  11. [11]
    I. Bredberg, T. Hartman, W. Song and A. Strominger, Black Hole Superradiance From Kerr/CFT, JHEP 04 (2010) 019 [arXiv:0907.3477] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    A. Castro, A. Maloney and A. Strominger, Hidden Conformal Symmetry of the Kerr Black Hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].
  13. [13]
    B. Chen and J. Long, Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence, JHEP 06 (2010) 018 [arXiv:1004.5039] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    W. Song and J. Xu, Correlation Functions of Warped CFT, JHEP 04 (2018) 067 [arXiv:1706.07621] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    A. Pathak, A.P. Porfyriadis, A. Strominger and O. Varela, Logarithmic corrections to black hole entropy from Kerr/CFT, JHEP 04 (2017) 090 [arXiv:1612.04833] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    A. Castro, C. Keeler and P. Szepietowski, Tweaking one-loop determinants in AdS 3, JHEP 10 (2017) 070 [arXiv:1707.06245] [INSPIRE].
  17. [17]
    G. Compere and S. Detournay, Semi-classical central charge in topologically massive gravity, Class. Quant. Grav. 26 (2009) 012001 [Erratum ibid. 26 (2009) 139801] [arXiv:0808.1911] [INSPIRE].
  18. [18]
    G. Compère, W. Song and A. Strominger, New Boundary Conditions for AdS3, JHEP 05 (2013) 152 [arXiv:1303.2662] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    S. Detournay, D. Israel, J.M. Lapan and M. Romo, String Theory on Warped AdS 3 and Virasoro Resonances, JHEP 01 (2011) 030 [arXiv:1007.2781] [INSPIRE].
  20. [20]
    M. Guica and A. Strominger, Microscopic Realization of the Kerr/CFT Correspondence, JHEP 02 (2011) 010 [arXiv:1009.5039] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  21. [21]
    G. Compere, W. Song and A. Virmani, Microscopics of Extremal Kerr from Spinning M5 Branes, JHEP 10 (2011) 087 [arXiv:1010.0685] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    S. El-Showk and M. Guica, Kerr/CFT, dipole theories and nonrelativistic CFTs, JHEP 12 (2012) 009 [arXiv:1108.6091] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    W. Song and A. Strominger, D-brane Construction of the 5D NHEK Dual, JHEP 07 (2012) 176 [arXiv:1105.0431] [INSPIRE].
  24. [24]
    T. Azeyanagi, D.M. Hofman, W. Song and A. Strominger, The Spectrum of Strings on Warped AdS 3 × S 3, JHEP 04 (2013) 078 [arXiv:1207.5050] [INSPIRE].
  25. [25]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
  26. [26]
    M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys. 5 (2018) 048 [arXiv:1710.08415] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    A. Bzowski and M. Guica, The holographic interpretation of \( J\overline{T} \) -deformed CFTs, arXiv:1803.09753 [INSPIRE].
  28. [28]
    S. Chakraborty, A. Giveon and D. Kutasov, \( J\overline{T} \) deformed CF T 2 and string theory, JHEP 10 (2018) 057 [arXiv:1806.09667] [INSPIRE].
  29. [29]
    L. Apolo and W. Song, Strings on warped AdS 3 via \( \mathrm{J}\overline{\mathrm{T}} \) deformations, JHEP 10 (2018) 165 [arXiv:1806.10127] [INSPIRE].
  30. [30]
    A. Strominger, AdS 2 quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [INSPIRE].
  31. [31]
    T. Hartman and A. Strominger, Central Charge for AdS 2 Quantum Gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [INSPIRE].
  32. [32]
    A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic Description of AdS 2 Black Holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].
  33. [33]
    A. Castro and W. Song, Comments on AdS 2 Gravity, arXiv:1411.1948 [INSPIRE].
  34. [34]
    A.J. Amsel, G.T. Horowitz, D. Marolf and M.M. Roberts, No Dynamics in the Extremal Kerr Throat, JHEP 09 (2009) 044 [arXiv:0906.2376] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
  37. [37]
    O. Parcollet and A. Georges, Non-Fermi-liquid regime of a doped Mott insulator, Phys. Rev. B 59 (1999) 5341 [cond-mat/9806119].
  38. [38]
    A. Kitaev, A simple model of quantum holography, talks at KITP, 7 April 2015 and 27 May 2015.Google Scholar
  39. [39]
    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
  41. [41]
    S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
  42. [42]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
  43. [43]
    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
  44. [44]
    J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
  45. [45]
    A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
  47. [47]
    C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
  48. [48]
    Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    E. Witten, An SYK-Like Model Without Disorder, arXiv:1610.09758 [INSPIRE].
  50. [50]
    W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE].
  51. [51]
    I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
  52. [52]
    D.J. Gross and V. Rosenhaus, A Generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
  54. [54]
    C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum Chaos and Holographic Tensor Models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    G. Turiaci and H. Verlinde, Towards a 2d QFT Analog of the SYK Model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE].
  56. [56]
    J. Murugan, D. Stanford and E. Witten, More on Supersymmetric and 2d Analogs of the SYK Model, JHEP 08 (2017) 146 [arXiv:1706.05362] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    X. Chen, R. Fan, Y. Chen, H. Zhai and P. Zhang, Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model, Phys. Rev. Lett. 119 (2017) 207603 [arXiv:1705.03406] [INSPIRE].CrossRefGoogle Scholar
  58. [58]
    S.-K. Jian and H. Yao, Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization, Phys. Rev. Lett. 119 (2017) 206602 [arXiv:1703.02051] [INSPIRE].CrossRefGoogle Scholar
  59. [59]
    W. Cai, X.-H. Ge and G.-H. Yang, Diffusion in higher dimensional SYK model with complex fermions, JHEP 01 (2018) 076 [arXiv:1711.07903] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  60. [60]
    C. Peng, Vector models and generalized SYK models, JHEP 05 (2017) 129 [arXiv:1704.04223] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
  62. [62]
    J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  63. [63]
    A. Almheiri and B. Kang, Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes, JHEP 10 (2016) 052 [arXiv:1606.04108] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  64. [64]
    K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
  65. [65]
    D.M. Hofman and A. Strominger, Chiral Scale and Conformal Invariance in 2D Quantum Field Theory, Phys. Rev. Lett. 107 (2011) 161601 [arXiv:1107.2917] [INSPIRE].
  66. [66]
    P. Chaturvedi, I. Papadimitriou, W. Song and B. Yu, in progress.Google Scholar
  67. [67]
    M. Cvetič and I. Papadimitriou, AdS 2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
  68. [68]
    A. Gaikwad, L.K. Joshi, G. Mandal and S.R. Wadia, Holographic dual to charged SYK from 3D Gravity and Chern-Simons, arXiv:1802.07746 [INSPIRE].
  69. [69]
    D. Anninos, T. Anous and R.T. D’Agnolo, Marginal deformations & rotating horizons, JHEP 12 (2017) 095 [arXiv:1707.03380] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  70. [70]
    F. Larsen, A nAttractor Mechanism for nAdS 2/nCF T 1 Holography, arXiv:1806.06330 [INSPIRE].
  71. [71]
    A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS 2/nCF T 1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [INSPIRE].
  72. [72]
    K. Bulycheva, A note on the SYK model with complex fermions, JHEP 12 (2017) 069 [arXiv:1706.07411] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  73. [73]
    R. Bhattacharya, S. Chakrabarti, D.P. Jatkar and A. Kundu, SYK Model, Chaos and Conserved Charge, JHEP 11 (2017) 180 [arXiv:1709.07613] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  74. [74]
    D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 Black Holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
  75. [75]
    T. Azeyanagi, S. Detournay and M. Riegler, Warped Black Holes in Lower-Spin Gravity, arXiv:1801.07263 [INSPIRE].
  76. [76]
    G. Compère, W. Song and A. Strominger, Chiral Liouville Gravity, JHEP 05 (2013) 154 [arXiv:1303.2660] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  77. [77]
    A. Castro, D.M. Hofman and G. Sárosi, Warped Weyl fermion partition functions, JHEP 11 (2015) 129 [arXiv:1508.06302] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  78. [78]
    K. Jensen, Locality and anomalies in warped conformal field theory, JHEP 12 (2017) 111 [arXiv:1710.11626] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  79. [79]
    A. Castro, D.M. Hofman and N. Iqbal, Entanglement Entropy in Warped Conformal Field Theories, JHEP 02 (2016) 033 [arXiv:1511.00707] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  80. [80]
    W. Song, Q. Wen and J. Xu, Modifications to Holographic Entanglement Entropy in Warped CFT, JHEP 02 (2017) 067 [arXiv:1610.00727] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  81. [81]
    H. Afshar, S. Detournay, D. Grumiller and B. Oblak, Near-Horizon Geometry and Warped Conformal Symmetry, JHEP 03 (2016) 187 [arXiv:1512.08233] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  82. [82]
    L. Apolo and W. Song, Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms, JHEP 07 (2018) 112 [arXiv:1804.10525] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  83. [83]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  84. [84]
    A.N. Schellekens, Meromorphic C = 24 conformal field theories, Commun. Math. Phys. 153 (1993) 159 [hep-th/9205072] [INSPIRE].
  85. [85]
    E. Perlmutter, Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [arXiv:1602.08272] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  86. [86]
    E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [INSPIRE].
  87. [87]
    A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  88. [88]
    N. Benjamin, E. Dyer, A.L. Fitzpatrick, A. Maloney and E. Perlmutter, Small Black Holes and Near-Extremal CFTs, JHEP 08 (2016) 023 [arXiv:1603.08524] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  89. [89]
    W. Li, W. Song and A. Strominger, Chiral Gravity in Three Dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  90. [90]
    A. Maloney, W. Song and A. Strominger, Chiral Gravity, Log Gravity and Extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [INSPIRE].
  91. [91]
    V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2d CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [INSPIRE].
  92. [92]
    A.B. Zamolodchikov and A.B. Zamolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152 [INSPIRE].
  93. [93]
    T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the Conformal Bootstrap, JHEP 08 (2017) 136 [arXiv:1705.08408] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  94. [94]
    D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  95. [95]
    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].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina
  2. 2.Department of PhysicsHarvard UniversityCambridgeU.S.A.

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