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
Regge's 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.Comment: 8 pages, to be published in Phys. Lett. B, uuencoded compressed
postscript file