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Theoretical and Mathematical Physics

, Volume 197, Issue 2, pp 1650–1662 | Cite as

Notes on the Syk Model in Real Time

  • I. Ya. Aref’eva
  • I. V. Volovich
Article

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 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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