Geodesic
Revealing nonperturbative effects in the~SYK model
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 198-221

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{TMF_2019_201_2_a4,
     author = {I. Ya. Aref'eva and I. V. Volovich and M. A. Khramtsov},
     title = {Revealing nonperturbative effects in {the~SYK} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {198--221},
     publisher = {mathdoc},
     volume = {201},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a4/}
}
TY  - JOUR
AU  - I. Ya. Aref'eva
AU  - I. V. Volovich
AU  - M. A. Khramtsov
TI  - Revealing nonperturbative effects in the~SYK model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 198
EP  - 221
VL  - 201
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a4/
LA  - ru
ID  - TMF_2019_201_2_a4
ER  - 
%0 Journal Article
%A I. Ya. Aref'eva
%A I. V. Volovich
%A M. A. Khramtsov
%T Revealing nonperturbative effects in the~SYK model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 198-221
%V 201
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a4/
%G ru
%F TMF_2019_201_2_a4
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/