Coupling gauge theory to spinfoam 3d quantum gravity

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.