Holonomy observables in Ponzano-Regge type state sum models

TL;DR

This paper investigates group element observables in the Ponzano-Regge model, revealing their interpretation via Feynman diagrams on a sphere and connecting them to the no-gravity limit of Turaev-Viro and Chern-Simons theories.

Contribution

It introduces a new perspective on group element observables in Ponzano-Regge models, linking them to Feynman diagrams and the no-gravity limit of other topological quantum field theories.

Findings

Group element observables correspond to Feynman diagrams on a sphere.

These observables are related to the no-gravity limit of Turaev-Viro and Chern-Simons models.

Abstract

We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contrast them to the well studied observables on the spin labels. We elucidate this interpretation by showing how they arise from the no-gravity limit of the Turaev-Viro model and Chern-Simons theory.