Notes on the SYK model in real time

TL;DR

This paper discusses a nonperturbative real-time formulation of the SYK model, demonstrating its well-defined generating functional and analyzing its zero-dimensional case, large N expansion, and phase transitions.

Contribution

It introduces a real-time approach to the SYK model that remains well-defined after transformation to bilocal fields, enabling nonperturbative analysis.

Findings

Real-time generating functional is well-defined after bilocal transformation.

Large N expansion of the zero-dimensional SYK model is evaluated.

Phase transitions in the SYK model are investigated.

Abstract

Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it diverges after the transformation to the fermion bilocal fields. We point out that the generating functional of the SYK model in real time is well defined even after the transformation to the bilocal fields and it can be used for nonperturbative investigations of its properties. The SYK model in zero dimensions is studied, its large N expansion is evaluated and phase transitions are investigated.