A review of the large N limit of tensor models

TL;DR

This paper reviews recent breakthroughs in extending the 1/N expansion from matrix models to tensor models, enabling the study of higher-dimensional random geometries.

Contribution

It summarizes recent advances that establish a viable 1/N expansion for tensor models, broadening their applicability in quantum gravity and related fields.

Findings

Successful extension of 1/N expansion to tensor models

Enhanced understanding of higher-dimensional random geometries

Potential applications in quantum gravity and string theory

Abstract

Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies in the 1/N expansion introduced by 't Hooft. Random tensor models generalize random matrices to theories of random higher dimensional spaces. For a long time, no viable 1/N expansion for tensors was known and their success was limited. A series of recent results has changed this situation and the extension of the 1/N expansion to tensors has been achieved. We review these results in this paper.