Quantum Null Geometry and Gravity

TL;DR

This paper explores how quantizing gravity on null hypersurfaces leads to emergent conformal field theories with a central charge, revealing quantum aspects of spacetime geometry and the emergence of time.

Contribution

It introduces a novel framework linking null hypersurface quantization to CFTs, highlighting the role of area operators and the concept of 'embadons' in quantum gravity.

Findings

Null hypersurface quantization yields associated CFTs with non-zero central charge.

The central charge quantifies degrees of freedom along null rays.

Divergence in total central charge is resolved by a discrete area spectrum.

Abstract

In this work, we demonstrate that quantizing gravity on a null hypersurface leads to the emergence of a CFT associated with each null ray. This result stems from the ultralocal nature of null physics and is derived through a canonical analysis of the Raychaudhuri equation, interpreted as a constraint generating null time reparametrizations. The CFT exhibits a non-zero central charge, providing a mechanism for the quantum emergence of time in gravitational systems and an associated choice of vacuum state. Our analysis reveals that the central charge quantifies the degrees of freedom along each null ray. Throughout our investigation, the area element of a cut plays a crucial role, necessitating its treatment as a quantum operator due to its dynamic nature in phase space or because of quantum backreaction. Furthermore, we show that the total central charge diverges in a perturbative analysis due to the infinite number of null generators. This divergence is resolved if there is a discrete spectrum for the area form operator. We introduce the concept of `embadons' to denote these localized geometric units of area, the fundamental building blocks of geometry at a mesoscopic quantum gravity scale.