Flowing in Group Field Theory Space: a Review

TL;DR

This review discusses recent advances in renormalization techniques applied to Group Field Theories, highlighting their connection to quantum gravity models and the discovery of renormalizable theories through tensor model methods.

Contribution

It provides a comprehensive overview of the extension of renormalization methods to GFTs with closure constraints, emphasizing new insights into their renormalization group flows.

Findings

Identification of a rich landscape of renormalizable GFTs

Understanding of perturbative and non-perturbative RG flows in GFTs

Connection of GFTs to lattice gauge theories and quantum gravity models

Abstract

We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d \geq 3$. More precisely, we focus on GFTs with so-called closure constraint, which are closely related to lattice gauge theories and quantum gravity spin foam models. With the help of recent tensor model tools, a rich landscape of renormalizable theories has been unravelled. We review our current understanding of their renormalization group flows, at both perturbative and non-perturbative levels.