Asymptotic expansion of the multi-orientable random tensor model

TL;DR

This paper analyzes the asymptotic expansion of the multi-orientable random tensor model, classifying dominant configurations and performing enumeration to understand its behavior as tensor size grows.

Contribution

It provides the first detailed asymptotic expansion analysis for the multi-orientable tensor model, identifying dominant graph configurations and their enumeration.

Findings

Dominant configurations are classified by degree.

Asymptotic expansion terms are explicitly characterized.

Enumeration of tensor graphs is achieved for the model.

Abstract

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expansion in N, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.