Critical behavior of colored tensor models in the large N limit

TL;DR

This paper analyzes the critical behavior of colored tensor models at large N, revealing that their dominant triangulations resemble branched polymers and exhibit a universal critical phenomenon.

Contribution

It provides a detailed analysis of the leading order in colored tensor models, showing the proliferation of triangulations as colored trees and establishing their critical behavior.

Findings

Triangulations proliferate like colored trees

Leading order is summable and exhibits universal critical behavior

Dominant triangulations are branched polymers

Abstract

Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of D-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers.