Diagrammatic proof of the large $N$ melonic dominance in the SYK model

TL;DR

This paper provides a rigorous, diagrammatic proof demonstrating that in the large N limit of the SYK model, melonic graphs dominate, confirming a key theoretical aspect of the model through combinatorial analysis.

Contribution

It offers the first direct, combinatorial proof of melonic dominance in the SYK model's large N limit, advancing theoretical understanding.

Findings

Melonic graphs dominate the large N limit of the SYK model.

The proof is rigorous and diagrammatic, based on combinatorial analysis.

Confirms a key theoretical prediction about the SYK model.

Abstract

A crucial result on the celebrated Sachdev-Ye-Kitaev model is that its large $N$ limit is dominated by melonic graphs. In this letter we offer a rigorous, diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs.