The 1/N expansion of colored tensor models

TL;DR

This paper develops a 1/N expansion for a colored tensor model, revealing a topological hierarchy where simpler topologies dominate at large N, with leading contributions from graphs representing three-spheres.

Contribution

It provides the first systematic topological expansion for the Boulatov tensor model and identifies the dominant graphs in the large N limit.

Findings

Leading order graphs correspond to three-spheres S^3

Higher order contributions involve more complex topologies

Systematic expansion parallels matrix model techniques

Abstract

In this paper we perform the 1/N expansion of the colored three dimensional Boulatov tensor model. As in matrix models, we obtain a systematic topological expansion, with more and more complicated topologies suppressed by higher and higher powers of N. We compute the first orders of the expansion and prove that only graphs corresponding to three spheres S^3 contribute to the leading order in the large N limit.