2018/04/30 by Benjamin Bahr, Giovanni Rabuffo, Sebastian Steinhaus · 1 citation
Physics and Astronomy · #gr-qc #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.98.106026
published as Phys. Rev. D 98, 106026 (2018) · 24 pages, 13 figures; v2: references added, corrected counting of attractive / repulsive directions in RG flow; v3: matching published version (revised plots and more thorough discussion of background independent RG flow)
arxiv created 2019/01/10 · arxiv updated 2019/01/11
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 (α,Λ,G). We first consider the projection of the RG flow along the α 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 (α,Λ,G) space showing one repulsive and two attractive directions.