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TMF, 2019, Volume 201, Number 2, Pages 198–221 (Mi tmf9742)  

This article is cited in 2 scientific papers (total in 2 papers)

Revealing nonperturbative effects in the SYK model

I. Ya. Aref'eva, I. V. Volovich, M. A. Khramtsov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: In the large-$N$ limit, we study saddle points of two SYK chains coupled by an interaction that is nonlocal in Euclidean time. We study the free model with the order of the fermionic interaction $q=2$ analytically and also investigate the model with interaction in the case $q=4$ numerically. We show that in both cases, there is a nontrivial phase structure with an infinite number of phases. Each phase corresponds to a saddle point in the noninteracting two-replica SYK. The nontrivial saddle points have a nonzero value of the replica-nondiagonal correlator in the sense of quasiaveraging if the coupling between replicas is turned off. The nonlocal interaction between replicas thus provides a protocol for turning the nonperturbatively subleading effects in SYK into nonequilibrium configurations that dominate at large $N$. For comparison, we also study two SYK chains with local interaction for $q=2$ and $q=4$. We show that the $q=2$ model has a similar phase structure, while the phase structure differs in the $q=4$ model, dual to the traversable wormhole.

Keywords: SYK model, large-$N$ limit, nonperturbative effect, replica-nondiagonal solution, quasiaverage, spontaneous symmetry breaking.

Funding Agency Grant Number
Foundation for the Development of Theoretical Physics and Mathematics BASIS 17-15-566-1
The research of M. A. Khramtsov is supported by the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" (Project No. 17-15-566-1).


DOI: https://doi.org/10.4213/tmf9742

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English version:
Theoretical and Mathematical Physics, 2019, 201:2, 1585–1605

Bibliographic databases:

Received: 13.05.2019
Revised: 13.05.2019

Citation: I. Ya. Aref'eva, I. V. Volovich, M. A. Khramtsov, “Revealing nonperturbative effects in the SYK model”, TMF, 201:2 (2019), 198–221; Theoret. and Math. Phys., 201:2 (2019), 1585–1605

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. A. Khramtsov, “Spontaneous symmetry breaking in the Sachdev-Ye-Kitaev model”, Phys. Part. Nuclei, 51:4 (2020), 557–561  crossref  isi
    2. I. Aref'eva, I. Volovich, “Gas of baby universes in jt gravity and matrix models”, Symmetry-Basel, 12:6 (2020), 975  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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