The propagation kernel for strong coupling gravity

The strong coupling limit of Einstein gravity in d+1$d+1$ dimensions gives rise to a quantum theory where after factorization of the conformal factor mode SL(d,R)/SO(d)$\mathrm{SL}(d,\mathbb{R})/\mathrm{SO}(d)$ nonlinear sigma-models are spatially coupled by the diffeomorphism constraint. A functional integral representation for the theory?s propagation kernel is derived in completions of the proper time gauge which manifestly invokes only physical gauge invariant degrees of freedom. In the weak field limit it reduces to the propagation kernel of massless and transversal-traceless free fields. For strong fields a covariant normal coordinate expansion is developed which covers the configuration manifold globally. Its leading order approximant resembles a semiclassical propagation kernel but without the need to solve the classical constraints. The results have implications for the ground state structure of quantum gravity.