The microscopic dynamics of quantum space as a group field theory

TL;DR

This paper introduces the group field theory approach to quantum gravity, detailing its application to 3D Riemannian gravity, discussing 4D extensions, and highlighting recent results and open issues in the field.

Contribution

It provides an extended introduction to GFT, details the quantization of 3D gravity, and discusses recent progress and open questions in extending GFT to 4D quantum gravity.

Findings

Detailed GFT quantization of 3D Riemannian gravity

Discussion of current status of 4D GFT models

Summary of recent results and open issues in GFT research

Abstract

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on recent results obtained in this approach and related open issues, concerning both the mathematical definition of GFT models, and possible avenues towards extracting interesting physics from them.