Quantum Gravity on $dS_{3}$

TL;DR

This paper derives an exact partition function for quantum gravity on three-dimensional de Sitter space using Chern-Simons theory, revealing a discrete set of quantum fluctuations and a logarithmic correction to entropy consistent with dS/CFT predictions.

Contribution

It provides the first exact Euclidean partition function for quantum gravity on $dS_{3}$ and analyzes quantum fluctuations and entropy corrections in this setting.

Findings

Partition function matches semi-classical de Sitter entropy.

Quantum fluctuations are discrete point mass configurations.

Logarithmic correction to entropy with coefficient -1.

Abstract

We study quantum gravity on $dS_{3}$ using the Chern-Simons formulation of three -dimensional gravity. We derive an exact expression for the partition function for quantum gravity on $dS_{3}$ in a Euclidean path integral approach. We show that the topology of the space relevant for studying de Sitter entropy is a solid torus. The quantum fluctuations of de Sitter space are sectors of configurations of point masses taking a {\em discrete} set of values. The partition function gives the correct semi-classical entropy. The sub-leading correction to the entropy is logarithmic in horizon area, with a coefficient -1. We discuss this correction in detail, and show that the sub-leading correction to the entropy from the dS/CFT correspondence agrees with our result. A comparison with the corresponding results for the $AdS_{3}$ BTZ black hole is also presented.