Numerical evidence for a phase transition in 4d spin foam quantum gravity

TL;DR

This paper investigates the renormalization group flow of 4d spin foam quantum gravity, providing numerical evidence for a phase transition that could enable a continuum limit by restoring broken diffeomorphism symmetry.

Contribution

It offers the first numerical and analytical study of RG flows in 4d spin foam quantum gravity, revealing a phase transition and the potential for a continuum limit.

Findings

Evidence of a phase transition in the RG flow.

Restoration of diffeomorphism symmetry at the critical point.

Indications that the critical point may serve as a continuum limit.

Abstract

Building on recent advances in defining Wilsonian RG flows, and in particular the notion of scales, for background-independent theories, we present a first investigation of the renormalization of the 4d spin foam path integral for quantum gravity, both analytically and numerically. Focussing on a specific truncation of the model using a hypercubic lattice, we compute the RG flow and find strong indications for a phase transition, as well as an interesting interplay between the different observed phases and the (broken) diffeomorphism symmetry of the model. Most notably, it appears that the critical point between the phases, which is a fixed point of the RG flow, is precisely where broken diffeomorphism symmetry is restored, which suggests that it might allow for the definition a continuum limit of the quantum gravity theory.