Matrix model formulation of four dimensional gravity

TL;DR

This paper explores how higher rank tensor models can be related to four-dimensional quantum gravity, establishing conditions under which Feynman diagrams correspond to four-dimensional simplicial manifolds.

Contribution

It provides a framework linking rank-four tensor models to four-dimensional quantum gravity and specifies conditions for associating Feynman diagrams with 4D simplicial manifolds.

Findings

Identifies conditions for Feynman diagrams to represent 4D simplicial manifolds

Establishes a connection between tensor models and 4D quantum gravity

Extends matrix model ideas to higher dimensions

Abstract

The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity and the precise conditions allowing to associate a four-dimensional simplicial manifold to Feynman diagrams of a rank-four tensor model.