Geodesic
Notes on the~SYK model in real time
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 296-310

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We discuss a nonperturbative formulation of the Sachdev–Ye–Kitaev (SYK) model. The partition function of the model can be represented as a well-defined functional integral over Grassmann variables in Euclidean time, but it diverges after the transformation to fermion bilocal fields. We note that the generating functional of the SYK model in real time is well defined even after the transformation to bilocal fields and can be used for nonperturbative investigations of its properties. We study the SYK model in zero dimensions, evaluate its large-$N$ expansion, and investigate phase transitions.
Keywords: disorder model, $1/N$ expansion, Sachdev–Ye–Kitaev model. 
@article{TMF_2018_197_2_a8,
     author = {I. Ya. Aref'eva and I. V. Volovich},
     title = {Notes on {the~SYK} model in real time},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {296--310},
     publisher = {mathdoc},
     volume = {197},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a8/}
}
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I. Ya. Aref'eva; I. V. Volovich. Notes on the~SYK model in real time. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 296-310. http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a8/