Diffeomorphisms and spin foam models

TL;DR

This paper investigates how diffeomorphisms act on spin foam models, revealing residual symmetries in 3D that clarify divergences and renormalization, with implications for higher-dimensional models.

Contribution

It demonstrates the residual diffeomorphism action in 3D spin foam models and connects it to divergences and renormalization, providing a gauge fixing approach.

Findings

Residual diffeomorphism action explains divergences in 3D models

Gauge fixing clarifies the renormalization of Ponzano-Regge model

Implications for finite higher-dimensional spin foam models

Abstract

We study the action of diffeomorphisms on spin foam models. We prove that in 3 dimensions, there is a residual action of the diffeomorphisms that explains the naive divergences of state sum models. We present the gauge fixing of this symmetry and show that it explains the original renormalization of Ponzano-Regge model. We discuss the implication this action of diffeomorphisms has on higher dimensional spin foam models and especially the finite ones.