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

This article is cited in 4 scientific papers (total in 4 papers)

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:

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

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v197/i2/p296

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Ya. Aref'eva, I. V. Volovich, “Quasi-averages in Random Matrix Models”, Proc. Steklov Inst. Math., 306 (2019), 1–8  mathnet  crossref  crossref  mathscinet  isi
    2. V. V. Belokurov, E. T. Shavgulidze, “Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics”, Theoret. and Math. Phys., 200:3 (2019), 1324–1334  mathnet  crossref  crossref  adsnasa  isi  elib
    3. V. V. Zharinov, “Hamiltonian operators with zero-divergence constraints”, Theoret. and Math. Phys., 200:1 (2019), 923–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. I. Ya. Aref'eva, I. V. Volovich, M. A. Khramtsov, “Revealing nonperturbative effects in the SYK model”, Theoret. and Math. Phys., 201:2 (2019), 1585–1605  mathnet  crossref  crossref  mathscinet  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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