SYK Models and SYK-like Tensor Models with Global Symmetry

TL;DR

This paper investigates SYK and SYK-like tensor models with global symmetry, revealing emergent local symmetries, deriving effective actions, analyzing chaos, and exploring connections to 3D gravity.

Contribution

It introduces and analyzes SYK and tensor models with global symmetry, highlighting emergent local symmetries and their implications for low energy physics and chaos.

Findings

Global symmetry enhances to a local Kac-Moody symmetry at strong coupling

Derived low energy effective action for the models

Analyzed chaotic behavior and spectrum of four-point functions

Abstract

In this paper, we study an SYK model and an SYK-like tensor model with global symmetry. First, we study the large $N$ expansion of the bi-local collective action for the SYK model with manifest global symmetry. We show that the global symmetry is enhanced to a local symmetry at strong coupling limit, and the corresponding symmetry algebra is the Kac-Moody algebra. The emergent local symmetry together with the emergent reparametrization is spontaneously and explicit broken. This leads to a low energy effective action. We evaluate four point functions, and obtain spectrum of our model. We derive the low energy effective action and analyze the chaotic behavior of the four point functions. We also consider the recent 3D gravity conjecture for our model. We also introduce an SYK-like tensor model with global symmetry. We first study chaotic behavior of four point functions in various channels for the rank-3 case, and generalize this into a rank-$(q-1)$ tensor model.