Recovering the Newtonian potential

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.