Quantization of conical spaces in 3D gravity

Abstract

We discuss the quantization and holographic aspects of a class of conical spaces in 2+1 dimensional pure AdS gravity. These appear as topological solitons in the Chern-Simons formulation of the theory and are closely related to the recently studied conical solutions in higher spin gravity. We discuss the classical fluctuations around these solutions, which form exceptional coadjoint orbits of the asymptotic Virasoro group. We argue that the quantization of these solutions leads to nonunitary representations of the Virasoro algebra, on account of their having boundary graviton fluctuations which lower the energy. We propose a framework to quantize them in a semiclassical expansion in the inverse central charge, which we use to compute their one-loop corrected energies. Interestingly, the resulting Virasoro representations contain a null vector, thus providing an appearance of Kac's degenerate representations, which are nonunitary at large central charge, in the context of gravity. We match the computed quantum corrections in the bulk with the properties of a class of primaries in Kac's classification.

26 pages. V2: minor changes; references and calculational details added

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• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Geometric actions and flat space holography
• On 3d Bulk Geometry of Virasoro Coadjoint Orbits: Orbit invariant charges and Virasoro hair on locally AdS3 geometries
• 3D Gravity in a Box
• Asymptotically flat structure of hypergravity in three spacetime dimensions
• Conformal blocks from Wilson lines with loop corrections
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Hypersymmetry bounds and three-dimensional higher-spin black holes
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• Quantizing higher-spin gravity in free-field variables
• Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
• Rectangular W-(super)algebras and their representations
• Resurgence, Conformal Blocks, and the Sum over Geometries in Quantum Gravity
• Superconformal blocks from Wilson lines with loop corrections
• Conical spaces, modular invariance and $c_{p,1}$ holography
• Higher-spin gauge theories in three spacetime dimensions
• A note on the admissibility of complex BTZ metrics
• Integrable hierarchies, Hurwitz numbers and a branch point field in critical topologically massive gravity
• Moduli space of logarithmic states in critical massive gravities