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Revealing Nonperturbative Effects in the SYK Model

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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.

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Acknowledgments

The authors are grateful to Maria Tikhanovskaya and Valentin Zagrebnov for the useful discussions.

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Authors and Affiliations

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

    I. Ya. Aref’eva, I. V. Volovich & M. A. Khramtsov

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  1. I. Ya. Aref’eva
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  2. I. V. Volovich
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  3. M. A. Khramtsov
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Correspondence to I. Ya. Aref’eva, I. V. Volovich or M. A. Khramtsov.

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Conflicts of interest. The authors declare no conflicts of interest.

Additional information

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).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 2, pp. 198–221, November, 2019.

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Aref’eva, I.Y., Volovich, I.V. & Khramtsov, M.A. Revealing Nonperturbative Effects in the SYK Model. Theor Math Phys 201, 1585–1605 (2019). https://doi.org/10.1134/S0040577919110059

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