Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime

TL;DR

This paper investigates the renormalization group flow of a spin foam quantum gravity model with curvature, revealing fixed points that suggest potential pathways toward a consistent quantum gravity theory.

Contribution

It introduces a curvature-inclusive deformation of the EPRL-FK spin foam model and analyzes its RG flow, identifying fixed points in the parameter space.

Findings

Identifies a UV-attractive fixed point in the RG flow.

Finds a fixed point with one repulsive and two attractive directions in parameter space.

Demonstrates numerical evaluation of geometric observables on different discretizations.

Abstract

We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in the large-$j$-limit. The vertex amplitude is deformed to include a cosmological constant term. The state sum is reduced to describe a foliated spacetime whose spatial slices are flat, isotropic and homogeneous. The model admits a non-vanishing extrinsic curvature whereas the scale factor can expand or contract at successive time steps. The reduction of degrees of freedom allows a numerical evaluation of certain geometric observables on coarser and finer discretizations. Their comparison defines the renormalization group (RG) flow of the model in the parameters $(\alpha,\Lambda,G)$. We first consider the projection of the RG flow along the $\alpha$ direction, which shows a UV-attractive fixed point. Then, we extend our analysis to two- and three-dimensional parameter spaces. Most notably, we find the indications of a fixed point in the $(\alpha,\Lambda,G)$ space showing one repulsive and two attractive directions.