Nonlocal correlations for semiclassical states in loop quantum gravity

We compute the two-point correlation function of the area operator for semiclassical states of loop quantum gravity in the limit of large spins. The cases of intrinsic and extrinsic coherent states are considered, along with a new class of semiclassical states constructed as perturbations of Livine-Speziale coherent states. For the usual coherent states, the correlations are shown to be short-ranged, decaying exponentially with the distance. Introducing perturbations given by correlated elementary excitations and decays of the gravitational field along pairs of loops, we obtain new states that, while preserving the peakedness properties of the unperturbed states, can also display long-ranged correlations. The perturbed coherent states include examples reproducing the typical decay of correlations for quantum fluctuations of the geometry associated with free gravitons on a background metric. Such a behavior is a natural requirement for the compatibility of semiclassical states in quantum gravity with the physical regime pictured by perturbative quantum gravity.