Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model

TL;DR

This paper analyzes the combinatorial properties of graphs from the colored Sachdev-Ye-Kitaev model, providing asymptotic enumeration results that connect to higher-dimensional topological structures.

Contribution

It offers a detailed combinatorial study and asymptotic enumeration of graphs in the SYK model, linking these to higher-dimensional triangulations and generalizations of genus.

Findings

Asymptotic enumeration of SYK-related graphs

Connection between colored graphs and higher-dimensional triangulations

Enumeration results applicable to generalized unicellular maps

Abstract

We consider the graphs involved in the theoretical physics model known as the colored Sachdev-Ye-Kitaev (SYK) model. We study in detail their combinatorial properties at any order in the so-called $1/N$ expansion, and we enumerate these graphs asymptotically. Because of the duality between colored graphs involving $q+1$ colors and colored triangulations in dimension $q$, our results apply to the asymptotic enumeration of spaces that generalize unicellular maps - in the sense that they are obtained from a single building block - for which a higher-dimensional generalization of the genus is kept fixed.