3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory

TL;DR

This paper connects 3D spinfoam quantum gravity with matter fields to group field theories, showing how effective matter theories emerge from classical solutions and perturbations, hinting at curved spacetime interpretations.

Contribution

It demonstrates how matter coupled to 3D quantum gravity can be derived from group field theories and classical solutions, extending the understanding of spinfoam models.

Findings

Effective field theory can be recast as a matrix model.

Classical solutions generate matter dynamics from group field theory.

Some solutions imply matter on curved non-commutative spacetimes.

Abstract

An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models.