The complete $1/N$ expansion of a SYK--like tensor model

TL;DR

This paper derives the complete 1/N expansion for a SYK-like tensor model, detailing the structure of two and four point functions and showing how higher-order terms relate to leading order functions.

Contribution

It provides the full 1/N expansion of a SYK-like tensor model, including explicit formulas for two and four point functions at all orders.

Findings

Leading order two point function is a sum over melonic graphs.

Leading order relevant four point functions are sums over dressed ladder diagrams.

Higher order corrections can be expressed in terms of leading order functions.

Abstract

A SYK--like model close to the colored tensor models has recently been proposed \cite{Witten:2016iux}. Building on results obtained in tensor models \cite{GurSch}, we discuss the complete $1/N$ expansion of the model. We detail the two and four point functions at leading order. The leading order two point function is a sum over melonic graphs, and the leading order relevant four point functions are sums over dressed ladder diagrams. We then show that any order in the $1/N$ series of the two point function can be written solely in term of the leading order two and four point functions. The full $1/N$ expansion of arbitrary correlations can be obtained by similar methods.