Superspace worldline formalism approach to Quantum Gravity: dimensional reduction and Holography

Using the ADM formalism, we demonstrate that the Hamiltonian formulation of Quantum Gravity is exactly in the form of a worldline (WL) formalism in the superspace. We then show that the Keldysh partition function reduces to the partition function of Euclidean 3D gravity. After discussing the meaning of the time parameter, we show that in the gauge fields formalism, our Keldysh partition function reduces to a generating functional of a 2D Conformal Field Theory (CFT). This functional exhibits a minimal time-lapse proportional to the square root of the cosmological constant. From the viewpoint of the Chern-Simons/Liouville correspondence, we calculate the exchange of virtual gravitons between two massive probes from the cosmological boundary.