SU(2) potentials in quantum gravity

Abstract

We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. 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 $R$. 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.