Coupling gauge theory to spinfoam 3d quantum gravity

TL;DR

This paper develops a 3D spinfoam model coupling Yang-Mills theory with quantum gravity, enabling calculations of transition amplitudes and demonstrating a semiclassical limit matching the classical Yang-Mills action.

Contribution

It introduces a novel spinfoam model where gravity and Yang-Mills variables are assigned to the same simplices, improving upon previous models.

Findings

Partition function evaluated as a power series in coupling constants.

Model reproduces the classical Yang-Mills action in the semiclassical limit.

Provides transition amplitudes for spin network states.

Abstract

We construct a spinfoam model for Yang-Mills theory coupled to quantum gravity in three dimensional riemannian spacetime. We define the partition function of the coupled system as a power series in g_0^2 G that can be evaluated order by order using grasping rules and the recoupling theory. With respect to previous attempts in the literature, this model assigns the dynamical variables of gravity and Yang-Mills theory to the same simplices of the spinfoam, and it thus provides transition amplitudes for the spin network states of the canonical theory. For SU(2) Yang-Mills theory we show explicitly that the partition function has a semiclassical limit given by the Regge discretization of the classical Yang-Mills action.