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TMF, 2018, Volume 197, Number 2, Pages 296–310 (Mi tmf9533)  

Notes on the SYK model in real time

I. Ya. Aref'eva, I. V. Volovich

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

Abstract: 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

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This research was supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).


DOI: https://doi.org/10.4213/tmf9533

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English version:
Theoretical and Mathematical Physics, 2018, 197:2, 1650–1662

Bibliographic databases:

Document Type: Article
Received: 17.01.2018

Citation: I. Ya. Aref'eva, I. V. Volovich, “Notes on the SYK model in real time”, TMF, 197:2 (2018), 296–310; Theoret. and Math. Phys., 197:2 (2018), 1650–1662

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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