Coarse graining methods for spin net and spin foam models

TL;DR

This paper explores numerical renormalization techniques for spin foam models in quantum gravity, introducing new algorithms and analyzing gauge symmetry behavior and fixed points in simplified models.

Contribution

It applies Migdal-Kadanoff and Tensor Network Renormalization to spin foam models, introducing a Gauss constraint preserving algorithm and analyzing gauge symmetry and fixed points.

Findings

Identification of fixed points in simplified models

Development of a stable Gauss constraint preserving algorithm

Insights into gauge symmetry behavior under renormalization

Abstract

We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on finite Abelian groups and introduce `cutoff models' to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the Tensor Network Renormalization analysis, a new Gauss constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We also describe the fixed point structure and establish an equivalence of certain models.