Coupling gauge theory to spinfoam 3d quantum gravity

Understand

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.