# Liouville Quantum Gravity

## TL;DR

This paper proposes a three-dimensional quantum gravity model as a holographic dual to Liouville conformal field theory, revealing unique properties like the absence of a normalisable AdS3 vacuum and the presence of primary black holes.

## Contribution

It introduces a consistent, unitary 3D quantum gravity theory with negative cosmological constant based on Liouville CFT, highlighting novel features and universal interactions.

## Key findings

- No normalisable AdS3 vacuum exists in the model.
- Primary black holes with zero spin are present.
- Universal boundary graviton interactions are identified.

## Abstract

We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological constant has peculiar properties. The quantum theory has no normalisable AdS3 vacuum. The model contains primary black holes with zero spin. All states can be interpreted as black holes dressed with boundary gravitons. There is a unique universal interaction between these states consistent with unitarity and the conformal symmetry of the model. This theory of gravity, though conceptually isolated from other models of quantum gravity, is worth scrutinising.