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

Razvan Gurau

doi:10.1016/j.nuclphysb.2017.01.015

Abstract

A SYK–like model close to the colored tensor models has recently been proposed [1]. Building on results obtained in tensor models [2], 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.

Highlights

A tensor model version [1] of the SYK model [3, 4] has been recently proposed by Witten
This model is very similar to the colored tensor model (CTM) [8, 9], except that:
- the SYK–like model of [1] is formulated in terms of real fields, while the CTM is usually formulated in terms of complex fields

Summary

Introduction

A tensor model version [1] of the SYK model [3, 4] (see [5, 6, 7] for recent developments) has been recently proposed by Witten. The action of the SYK–like tensor model proposed in [1] in Euclidean time is: S=. This model is very similar to the colored tensor model (CTM) [8, 9], except that:. - the SYK–like model of [1] is formulated in terms of real fields, while the CTM is usually formulated in terms of complex fields. This slightly changes the 1/n expansion and we will briefly allude to this at the end of this paper. And we only discuss the case with at least four colors, D ≥ 3

Discussion

The two point function

The four point functions

Two point function at leading order

Findings

Four point functions at leading order