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

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

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
\Bibitem{AreVolKhr19} \by I.~Ya.~Aref'eva, I.~V.~Volovich, M.~A.~Khramtsov \paper Revealing nonperturbative effects in the~SYK model \jour TMF \yr 2019 \vol 201 \issue 2 \pages 198--221 \mathnet{http://mi.mathnet.ru/tmf9742} \crossref{https://doi.org/10.4213/tmf9742} \transl \jour Theoret. and Math. Phys. \yr 2019 \vol 201 \issue 2 \pages 1585--1605