A review of the 1/N expansion in random tensor models

TL;DR

This paper reviews recent advances in tensor models, highlighting the development of a 1/N expansion in higher dimensions that enables analytical control over random topological spaces, similar to matrix models in 2D.

Contribution

It discusses the recent breakthrough establishing a 1/N expansion for complex tensor models in arbitrary dimensions, allowing for controlled analysis of higher-dimensional random geometries.

Findings

1/N expansion dominated by spherical topology graphs

Tensor models undergo phase transition to continuum theory

Analytical control achieved for higher-dimensional random spaces

Abstract

Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry, etc. Their success relies crucially on the so called 1/N expansion introduced by 't Hooft. In higher dimensions matrix models generalize to tensor models. In the absence of a viable 1/N expansion tensor models have for a long time been less successful in providing an analytically controlled theory of random higher dimensional topological spaces. This situation has drastically changed recently. Models for a generic complex tensor have been shown to admit a 1/N expansion dominated by graphs of spherical topology in arbitrary dimensions and to undergo a phase transition to a continuum theory.