On Holomorphic Factorization in Asymptotically AdS 3D Gravity

Abstract

This paper studies aspects of ``holography'' for Euclidean signature pure gravity on asymptotically AdS 3-manifolds. This theory can be described as SL(2,C) CS theory. However, not all configurations of CS theory correspond to asymptotically AdS 3-manifolds. We show that configurations that do have the metric interpretation are parameterized by the so-called projective structures on the boundary. The corresponding asymptotic phase space is shown to be the cotangent bundle over the Schottky space of the boundary. This singles out a ``gravitational'' sector of the SL(2,C) CS theory. It is over this sector that the path integral has to be taken to obtain the gravity partition function. We sketch an argument for holomorphic factorization of this partition function.

32+1 pages, no figures; (v2) one reference added, a statement regarding priorities modified; (v3) presentational changes, an important sign mistake corrected

References in corpus (3)

• Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
• On the Boundary Dynamics of Chern-Simons Gravity
• Lambda<0 Quantum Gravity in 2+1 Dimensions I: Quantum States and Stringy S-Matrix

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• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity
• On the Chaos Bound in Rotating Black Holes
• Energy Reflection and Transmission at 2D Holographic Interfaces
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• Holographic boundary actions in AdS${}_3$/CFT${}_2$ revisited
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• Virasoro Entanglement Berry Phases
• 6D Interpretation of 3D Gravity
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• 2D Conformal Field Theories and Holography
• Entanglement Entropy with a Time-dependent Hamiltonian
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