Liouville Quantum Gravity

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.

arXiv comment26 pages, journal version

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• Conical spaces, modular invariance and $c_{p,1}$ holography
• Pure and Twisted Holography
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• String Scale Thermal Anti-de Sitter Spaces
• Phase space holography with no strings attached
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
• Holographic JT gravity with quartic couplings
• Liouville theory on a horizon: point particle/scalar field duality and Page-like curve
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics