# SYK-like Tensor Models on the Lattice

## TL;DR

This paper investigates large N tensor models on the lattice, analyzing their four-point functions, spectra, and behaviors, revealing similarities and differences with the SYK model, and extending results to higher ranks and corrections.

## Contribution

It introduces techniques for analyzing lattice tensor models without disorder and applies them to various models, including new interpolations and higher-rank generalizations.

## Key findings

- Computed four-point functions at large N and strong coupling.
- Identified spectral properties and long-time behaviors.
- Extended analysis to rank-D tensor models and higher-order corrections.

## Abstract

We study large $N$ tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large $N$ and strong coupling, and discuss their spectrum and long time behaviors. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-$D$ tensor models where we obtain analogous results as $D=3$ case for the four point functions which we computed. For $D>5$, we are able to compute the next-to-subleading ${1 \over N}$ corrections for a specific four point function.