Group field theory formulation of 3d quantum gravity coupled to matter fields

TL;DR

This paper introduces a new group field theory model for 3d quantum gravity coupled with matter, producing a unified framework that combines spacetime geometry and matter interactions through spin foam amplitudes.

Contribution

It develops a novel group field theory formulation that simultaneously describes 3d quantum gravity and matter fields with arbitrary spin and mass.

Findings

Produces fat graphs encoding spacetime and matter interactions

Reconstructs 3D simplicial complexes from algebraic data

Provides quantum amplitudes for gravity coupled to massive spinning particles

Abstract

We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss.