A definition of the Ponzano-Regge quantum gravity model in terms of surfaces

TL;DR

This paper reformulates the Ponzano-Regge quantum gravity model's partition function as a sum over surfaces in 2+1 dimensions, providing a geometric interpretation of divergences.

Contribution

It introduces a surface-based formulation of the Ponzano-Regge model and offers a geometric understanding of its divergences.

Findings

Partition function expressed as sum over surfaces

Geometric interpretation of divergences

Provides new insights into 3D quantum gravity models

Abstract

We show that the partition function of the Ponzano-Regge quantum gravity model can be written as a sum over surfaces in a $(2+1)$ dimensional space-time. We suggest a geometrical meaning, in terms of surfaces, for the (regulated) divergences that appear in the partition function.