Functional Renormalisation Group analysis of Tensorial Group Field Theories on $\mathbb{R}^d$

TL;DR

This paper applies functional renormalisation group methods to tensorial group field theories on , analyzing their phase structure and fixed points to understand their potential for quantum gravity and emergent spacetime.

Contribution

It provides the first renormalisation group analysis of TGFTs on  with gauge invariance, identifying phase transitions and fixed points in their phase diagram.

Findings

Existence of UV and IR fixed points in studied models

Evidence of phase transition of condensation type

Mapping of phase diagram in a simple truncation

Abstract

Rank-d Tensorial Group Field Theories are quantum field theories defined on a group manifold $G^{\times d}$, which represent a non-local generalization of standard QFT, and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalisation analysis is crucial both for establishing their consistency as quantum field theories, and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalisation group flow of two simple classes of TGFTs, defined for the group $G=\mathbb{R}$ for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalisation group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.