A group field theory for 3d quantum gravity coupled to a scalar field

TL;DR

This paper introduces a novel group field theory model that unifies 3D quantum gravity with scalar matter fields, extending previous models and providing a framework for coupled gravity-matter quantum amplitudes.

Contribution

It develops a new group field theory generalising the Boulatov model to include matter coupling, bridging quantum gravity and matter fields in 3D.

Findings

Feynman amplitudes match Riemannian quantum gravity spin foam amplitudes with matter

Model generalises Boulatov's approach to include scalar fields

Provides a basis for future extensions and analysis of coupled quantum gravity-matter systems

Abstract

We present a new group field theory model, generalising the Boulatov model, which incorporates both 3-dimensional gravity and matter coupled to gravity. We show that the Feynman diagram amplitudes of this model are given by Riemannian quantum gravity spin foam amplitudes coupled to a scalar matter field. We briefly discuss the features of this model and its possible generalisations.