# Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders

## TL;DR

This paper applies tensor diagrammatic methods to analyze the leading and next-to-leading order contributions in colored SYK and Gurau-Witten tensor models, providing a systematic approach to their large N expansions.

## Contribution

It introduces a diagrammatic method from tensor theory to identify key contributions in colored SYK and Gurau-Witten models at large N, extending previous analytical techniques.

## Key findings

- Identified all leading and next-to-leading order diagrams for 2- and 4-point functions in colored SYK.
- Extended the diagrammatic approach to Gurau-Witten tensor models, revealing increased complexity.
- Demonstrated the applicability of tensor methods to analyze complex fermionic models.

## Abstract

The Sachdev-Ye-Kitaev (SYK) model is a model of $q$ interacting fermions. Gross and Rosenhaus have proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, those flavors are reminiscent of the colors used in random tensor theory. This gives us the opportunity to apply some modern, yet elementary, tools developed in the context of random tensors to one particular instance of such colored SYK models. We illustrate our method by identifying all diagrams which contribute to the leading and next-to-leading orders of the 2-point and 4-point functions in the large $N$ expansion, and argue that our method can be further applied if necessary. In a second part we focus on the recently introduced Gurau-Witten tensor model and also extract the leading and next-to-leading orders of the 2-point and 4-point functions. This analysis turns out to be remarkably more involved than in the colored SYK model.