Geodesic
Revealing nonperturbative effects in the SYK model
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 198-221 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, quasiaverage, spontaneous symmetry breaking.
Mots-clés : nonperturbative effect, replica-nondiagonal solution 
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I. Ya. Aref'eva; I. V. Volovich; M. A. Khramtsov. Revealing nonperturbative effects in the SYK model. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 198-221. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a4/

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