The emergence of background geometry from quantum fluctuations

TL;DR

This paper demonstrates how quantizing two-dimensional gravity results in a quantum space-time with a constant negative curvature, naturally producing the Hartle-Hawking boundary condition.

Contribution

It reveals the emergence of background geometry from quantum fluctuations in two-dimensional gravity, connecting quantum effects to classical geometric structures.

Findings

Quantum fluctuations induce a space-time with negative curvature.

The Hartle-Hawking boundary condition arises naturally from quantization.

Average geometry corresponds to constant negative curvature.

Abstract

We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space-time where the average geometry is that of constant negative curvature and where the Hartle-Hawking boundary condition arises naturally.