Functional Renormalisation Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

TL;DR

This paper applies the Functional Renormalisation Group to a Tensorial Group Field Theory on , revealing IR and UV fixed points and suggesting a phase transition from symmetric to condensate phase.

Contribution

It is the first to implement a renormalisation procedure on a TGFT model over a non-compact group manifold, addressing IR divergences via compactification.

Findings

Identification of IR and UV fixed points in the RG flow

Evidence of a phase transition from symmetric to condensate phase

Regularisation of IR divergences through compactification

Abstract

We study a model of Tensorial Group Field Theory (TGFT) on $\mathbb{R}^3$ from the point of view of the Functional Renormalisation Group. This is the first attempt to apply a renormalisation procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on $\mathbb{R}$) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.