Continuum spin foam model for 3d gravity

TL;DR

This paper presents a continuum spin foam model for 3d gravity that aligns with canonical loop quantization, using a background-independent covariant framework with a renormalized sum over polyhedra, and is equivalent to the Turaev-Viro model.

Contribution

It introduces a continuum spin foam framework for 3d gravity that avoids background structures and connects covariant and canonical quantizations.

Findings

The model induces the kinematics of canonical loop quantization.

The dynamics are generated by a renormalized sum over colored polyhedra.

The resulting model is projectively equivalent to the Turaev-Viro model.

Abstract

An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a {\em renormalized} sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e. g. triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is {\em projectively} equivalent to the Turaev-Viro model.