A combinatorial and field theoretic path to quantum gravity: the new challenges of group field theory

TL;DR

This paper discusses the development and challenges of group field theories, a promising approach in quantum gravity research that connects loop quantum gravity and simplicial quantum gravity.

Contribution

It introduces the GFT formalism and outlines key open issues and challenges for future research in the field.

Findings

GFT formalism links different quantum gravity approaches

Identifies open mathematical and physical challenges in GFT

Highlights potential for interdisciplinary research

Abstract

Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link between different approaches such as loop quantum gravity and simplicial quantum gravity. After a brief introduction to the GFT formalism we put forward a long but still far from exhaustive list of open issues that this line of research faces, and that could be represent interesting challenges for mathematicians and mathematical physicists alike.