Review on the Operator/Feynman diagram/Dessins d'enfant Correspondence in Tensor Model

TL;DR

This paper reviews the operator/Feynman diagram/dessin d'enfants correspondence in rank 3 tensor models, introduces cut & join operations in this context, and classifies operators up to level 5 using dessins d'enfants.

Contribution

It provides a comprehensive review of the correspondence and extends the classification of tensor model operators using dessins d'enfants up to level 5.

Findings

Classification of operators up to level 5

Introduction of cut & join operations in dessins d'enfants

Clarification of the operator/Feynman diagram/dessin d'enfants correspondence

Abstract

A short review of the Operator/Feynman diagram/dessin d'enfants correspondence in the rank 3 tensor model is presented, and the cut & join operation is given in the language of dessin d'enfants as a straightforward development. We classify operators of the rank 3 tensor model up to level 5 with dessin d'enfants.