On the replica structure of Sachdev-Ye-Kitaev model

Hanteng Wang, D. Bagrets, A. L. Chudnovskiy, A. Kamenev

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We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.

Original languageEnglish (US)
Article number57
JournalJournal of High Energy Physics
Issue number9
StatePublished - Sep 1 2019

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2019, The Author(s).


  • Field Theories in Lower Dimensions
  • Holography and condensed matter physics (AdS/CMT)
  • Random Systems


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