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

TL;DR

This paper presents a novel superspace worldline formalism for Quantum Gravity, revealing dimensional reduction to 3D gravity and a connection to 2D CFTs, with implications for holography and quantum boundary interactions.

Contribution

It introduces a superspace worldline approach to Quantum Gravity, demonstrating dimensional reduction and linking Hamiltonian formalism to holographic dualities.

Findings

Hamiltonian Quantum Gravity matches a worldline formalism in superspace.

Keldysh partition function reduces to 3D Euclidean gravity partition function.

Functional relates to a 2D CFT with minimal time-lapse proportional to the square root of the cosmological constant.

Abstract

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.