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SYK-like tensor models on the lattice

  • Prithvi Narayan
  • Junggi Yoon
Open Access
Regular Article - Theoretical Physics

Abstract

We study large N tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large N and strong coupling, and discuss their spectrum and long time behaviors. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-D tensor models where we obtain analogous results as D = 3 case for the four point functions which we computed. For D > 5, we are able to compute the next-to-subleading \( \frac{1}{N} \) corrections for a specific four point function.

Keywords

1/N Expansion Field Theories in Lower Dimensions Matrix Models 

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]
    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].
  2. [2]
    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk at KITP seminar, http://online.kitp.ucsb.edu/online/joint98/kitaev/, U.S.A., 12 February 2015.
  4. [4]
    A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev/, U.S.A., 7 April 2015.
  5. [5]
    A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/, U.S.A., 27 May 2015.
  6. [6]
    S. Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].CrossRefGoogle Scholar
  7. [7]
    J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    A. Jevicki, K. Suzuki and J. Yoon, Bi-local holography in the SYK model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].ADSGoogle Scholar
  10. [10]
    A. Jevicki and K. Suzuki, Bi-local holography in the SYK model: perturbations, JHEP 11 (2016) 046 [arXiv:1608.07567] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  11. [11]
    J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, Prog. Theor. Exp. Phys. 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
  15. [15]
    K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    G. Mandal, P. Nayak and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, arXiv:1702.04266 [INSPIRE].
  17. [17]
    S.R. Das, A. Jevicki and K. Suzuki, Three dimensional view of the SYK/AdS duality, arXiv:1704.07208 [INSPIRE].
  18. [18]
    D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    S. Banerjee and E. Altman, Solvable model for a dynamical quantum phase transition from fast to slow scrambling, Phys. Rev. B 95 (2017) 134302 [arXiv:1610.04619] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [Addendum ibid. D 95 (2017) 069904] [arXiv:1610.08917] [INSPIRE].
  21. [21]
    T. Nishinaka and S. Terashima, A note on Sachdev-Ye-Kitaev like model without random coupling, arXiv:1611.10290 [INSPIRE].
  22. [22]
    T. Li, J. Liu, Y. Xin and Y. Zhou, Supersymmetric SYK model and random matrix theory, JHEP 06 (2017) 111 [arXiv:1702.01738] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    R. Gurau, Quenched equals annealed at leading order in the colored SYK model, arXiv:1702.04228 [INSPIRE].
  24. [24]
    V. Bonzom, L. Lionni and A. Tanasa, Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders, J. Math. Phys. 58 (2017) 052301 [arXiv:1702.06944] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    C. Peng, Vector models and generalized SYK models, JHEP 05 (2017) 129 [arXiv:1704.04223] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    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].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    M. Berkooz, P. Narayan, M. Rozali and J. Simón, Higher dimensional generalizations of the SYK model, JHEP 01 (2017) 138 [arXiv:1610.02422] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    G. Turiaci and H. Verlinde, Towards a 2d QFT analog of the SYK model, arXiv:1701.00528 [INSPIRE].
  29. [29]
    M. Berkooz, P. Narayan, M. Rozali and J. Simón, Comments on the random Thirring model, arXiv:1702.05105 [INSPIRE].
  30. [30]
    Y. Gu, A. Lucas and X.-L. Qi, Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains, SciPost Phys. 2 (2017) 018 [arXiv:1702.08462] [INSPIRE].CrossRefGoogle Scholar
  31. [31]
    R. Gurau, Colored group field theory, Commun. Math. Phys. 304 (2011) 69 [arXiv:0907.2582] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    R. Gurau and V. Rivasseau, The 1/N expansion of colored tensor models in arbitrary dimension, Europhys. Lett. 95 (2011) 50004 [arXiv:1101.4182] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    R. Gurau, The complete 1/N expansion of colored tensor models in arbitrary dimension, Annales Henri Poincaré 13 (2012) 399 [arXiv:1102.5759] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    V. Bonzom, R. Gurau, A. Riello and V. Rivasseau, Critical behavior of colored tensor models in the large-N limit, Nucl. Phys. B 853 (2011) 174 [arXiv:1105.3122] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    R. Gurau and J.P. Ryan, Colored tensor models — a review, SIGMA 8 (2012) 020 [arXiv:1109.4812] [INSPIRE].MathSciNetMATHGoogle Scholar
  36. [36]
    R. Gurau, Universality for random tensors, Ann. Inst. H. Poincaré Probab. Statist. 50 (2014) 1474 [arXiv:1111.0519] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    V. Bonzom, R. Gurau and V. Rivasseau, Random tensor models in the large-N limit: uncoloring the colored tensor models, Phys. Rev. D 85 (2012) 084037 [arXiv:1202.3637] [INSPIRE].ADSGoogle Scholar
  38. [38]
    R. Gurau and G. Schaeffer, Regular colored graphs of positive degree, Ann. Inst. H. Poincaré Comb. Phys. Interact. 3 (2016) 257 [arXiv:1307.5279].MathSciNetCrossRefMATHGoogle Scholar
  39. [39]
    S. Carrozza and A. Tanasa, O(N ) random tensor models, Lett. Math. Phys. 106 (2016) 1531 [arXiv:1512.06718] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    R. Gurau, The complete 1/N expansion of a SYK-like tensor model, Nucl. Phys. B 916 (2017) 386 [arXiv:1611.04032] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    V. Bonzom and S. Dartois, Blobbed topological recursion for the quartic melonic tensor model, arXiv:1612.04624 [INSPIRE].
  42. [42]
    E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE].
  43. [43]
    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].ADSGoogle Scholar
  44. [44]
    C. Peng, M. Spradlin and A. Volovich, A supersymmetric SYK-like tensor model, JHEP 05 (2017) 062 [arXiv:1612.03851] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    C. Krishnan, K.V.P. Kumar and S. Sanyal, Random matrices and holographic tensor models, JHEP 06 (2017) 036 [arXiv:1703.08155] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum chaos and holographic tensor models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    S. Chaudhuri, V.I. Giraldo-Rivera, A. Joseph, R. Loganayagam and J. Yoon, Abelian tensor models on the lattice, arXiv:1705.01930 [INSPIRE].
  48. [48]
    F. Ferrari, The large D limit of planar diagrams, arXiv:1701.01171 [INSPIRE].
  49. [49]
    H. Itoyama, A. Mironov and A. Morozov, Rainbow tensor model with enhanced symmetry and extreme melonic dominance, Phys. Lett. B 771 (2017) 180 [arXiv:1703.04983] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    H. Itoyama, A. Mironov and A. Morozov, Ward identities and combinatorics of rainbow tensor models, JHEP 06 (2017) 115 [arXiv:1704.08648] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    I.R. Klebanov and A.A. Tseytlin, Intersecting M-branes as four-dimensional black holes, Nucl. Phys. B 475 (1996) 179 [hep-th/9604166] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    M. Beccaria and A.A. Tseytlin, Partition function of free conformal fields in 3-plet representation, JHEP 05 (2017) 053 [arXiv:1703.04460] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    R. Gurau, The 1/N expansion of colored tensor models, Annales Henri Poincaré 12 (2011) 829 [arXiv:1011.2726] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  54. [54]
    S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    M. Blake, Universal charge diffusion and the butterfly effect in holographic theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    M. Blake, Universal diffusion in incoherent black holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE].ADSGoogle Scholar
  57. [57]
    S.-K. Jian and H. Yao, Solvable SYK models in higher dimensions: a new type of many-body localization transition, arXiv:1703.02051 [INSPIRE].
  58. [58]
    C.-M. Jian, Z. Bi and C. Xu, A model for continuous thermal metal to insulator transition, arXiv:1703.07793 [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.International Centre for Theoretical Sciences (ICTS-TIFR)BengaluruIndia

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