3.12 Recovering the Newtonian potential

Hamber and Williams [121] used an ansatz coming from a weak-field calculation for the amplitude of two gravitationally interacting particles separated by a fixed geodesic distance. They used the ldl-measure on a 164-lattice, with λ = 1 and a = 0. The potential V(d) is extracted from the connected Wilson-line to Wilson-line correlator. From data in d ∈ [0,5], and for sufficiently large k, one finds an attractive potential V (d) < 0. They considered fits to various shapes of the potential V, in order to extract an effective Newton’s constant. – They also suggested an effective action for ℛ depending on k, λ and a that shares some of the features observed in the simulations.
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