The Multi-Orientable Random Tensor Model, a Review

TL;DR

This review discusses the development and key results of the multi-orientable tensor model, including its large N expansion, combinatorial analysis, and double scaling limit, positioning it as a significant alternative to colored tensor models.

Contribution

It provides a comprehensive review of the multi-orientable tensor model's theoretical advancements and analytical techniques, highlighting its potential as an alternative framework.

Findings

Implementation of the 1/N expansion and large N limit

Combinatorial analysis of tensor model terms

Development of a double scaling limit

Abstract

After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the $1/N$ expansion and of the large $N$ limit ($N$ being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.