Group field theory formulation of 3d quantum gravity coupled to matter fields
Daniele Oriti, James Ryan
TL;DR
The paper constructs a Boulatov-type group field theory that extends 3d quantum gravity to include matter fields of arbitrary spin and mass. By introducing a coupled field with momentum degrees of freedom, the model generates Feynman diagrams whose amplitudes reproduce Coupled Ponzano–Regge spin foam amplitudes, integrating gravity and matter on a common simplicial scaffold. Key features include explicit momentum conservation at particle vertices, a dual particle graph framework, and the ability to host multiple particle species and scalar reductions; the formalism also discusses DSU(2) structures and potential noncommutative effective field theories. This work strengthens the bridge between group field theory, spin foams, and quantum gravity phenomenology, and sets the stage for generalizations to higher dimensions and gauge interactions. The results imply a pathway to phenomenology via effective noncommutative matter theories derived from quantum gravity and motivate further exploration of gravity-matter symmetries within GFT.
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.