Bi-Local Holography in the SYK Model

TL;DR

This paper develops a bi-local holographic framework for the SYK model, establishing Feynman rules and diagrammatic techniques that connect the model to dual AdS theories, enhancing understanding of holography at large N.

Contribution

It introduces a systematic bi-local Feynman rule approach for the SYK model, linking it to dual AdS holography and enabling calculations at IR fixed points.

Findings

Established 1/N Feynman rules using bi-local propagators.

Connected bi-local diagrams to Witten diagrams in AdS.

Demonstrated applicability at IR fixed points and off.

Abstract

We discuss large $N$ rules of the Sachdev-Ye-Kitaev model and the bi-local representation of holography of this theory. This is done by establishing $1/N$ Feynman rules in terms of bi-local propagators and vertices, which can be evaluated following the recent procedure of Polchinski and Rosenhaus. These rules can be interpreted as Witten type diagrams of the dual AdS theory, which we are able to define at IR fixed point and off.