3D Gravity in a Box

Abstract

The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are "more local" than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to $T\overline{T}$-deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS${}_3$ gravity. This algebra should be obeyed by the stress tensor in any $T\overline{T}$-deformed holographic CFT. We next initiate quantization of this system within the general framework of coadjoint orbits, obtaining - in perturbation theory - a deformed version of the Alekseev-Shatashvili symplectic form and its associated geometric action. The resulting energy spectrum is consistent with the expected spectrum of $T\overline{T}$-deformed theories, although we only carry out the explicit comparison to $\mathcal{O}(1/\sqrt{c})$ in the $1/c$ expansion.

arXiv comment59 pages, corrected typos and minus signs. This is the published version

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• Field Theory of Interacting Boundary Gravitons
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Glue-on AdS holography for $T\bar{T}$-deformed CFTs
• Holographic entanglement entropy in $T\overline{T}$-deformed AdS${}_3$
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• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• Virasoro Entanglement Berry Phases
• Flows in the Space of Interacting Chiral Boson Theories
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• Probing holography in $p$-adic CFT
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