More On Pure Gravity with a Negative Cosmological Constant

TL;DR

This paper explores the subtleties in the Chern-Simons formulation of 3D pure gravity with negative cosmological constant, clarifying its classical and quantum equivalences with Liouville theory and addressing stability issues.

Contribution

It identifies an automorphism ambiguity affecting the theory's stability and refines the understanding of the gravity-Liouville correspondence both classically and quantum mechanically.

Findings

Clarified the automorphism ambiguity in the Chern-Simons formulation.

Revisited classical and quantum equivalences with Liouville theory.

Proposed Liouville CFT as a stable definition of 3D pure gravity.

Abstract

We identify an ambiguity in the Chern-Simons formulation of three-dimensional gravity with negative cosmological constant that originates in an outer automorphism of the Lie algebra sl(2,R). It has important consequences for the stability of the theory in a space-time with boundary. We revisit the classical equivalence of three-dimensional gravity with a boundary Liouville theory both on and off the mass shell. Moreover, we provide further details on the quantum equivalence, the gauge symmetry that renders the spectrum diagonal, as well as the relation between asymptotically AdS3 metrics and polar boundary conditions. We thus set the proposal that the Liouville conformal field theory serves as a definition of a unitary theory of pure gravity in three dimensions with negative cosmological constant on a more stable footing.