Large-$N$ limit of $O(N)^3$-invariant general sextic tensor model

TL;DR

This paper analyzes a broad class of sextic tensor models with $O(N)^3$ symmetry, identifying dominant graph structures in the large-$N$ limit, including new tensor graph types beyond melonic and tadpole graphs.

Contribution

It extends the large-$N$ analysis to all connected sextic interactions with $O(N)^3$ symmetry, revealing new dominant graph structures.

Findings

Identified dominant graphs in the large-$N$ limit, including new tensor graph types.

Extended tensorial intermediate field method to all connected sextic interactions except wheel.

Explicitly characterized the large-$N$ behavior of the $O(N)^3$-invariant sextic tensor model.

Abstract

We study a sextic tensor model where the interaction terms are given by all $O(N)^3$-invariant bubbles. The class of invariants studied here is thus a larger one that the class of the $U(N)^3$-invariant sextic tensor model. We implement the large $N$ limit mechanism for this general model and we explicitly identify the dominant graphs in the $1/N$ expansion. This class of dominant graphs contains tadpole graphs, melonic graphs but also new types of tensor graphs. Our analysis adapts the tensorial intermediate field method, previously applied only to the prismatic interaction, to all connected sextic interactions except the wheel interaction, which we treat separately using a cycle analysis.