Static quark potentials in quantum gravity

We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on 63 × 4 and 83 × 4 simplicial lattices. The action consists of the gravitational term given by Reggeʹs discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants mp2 and β respectively. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance R. We compare potentials on a flat simplicial lattice with those on a fluctuating Regge skeleton. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.