SciPost Submission Page
3D Gravity in a Box
by Per Kraus, Ruben Monten, Richard M. Myers
 Published as SciPost Phys. 11, 070 (2021)
Submission summary
As Contributors:  Per Kraus · Ruben Monten 
Arxiv Link:  https://arxiv.org/abs/2103.13398v3 (pdf) 
Date accepted:  20210908 
Date submitted:  20210830 02:51 
Submitted by:  Monten, Ruben 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
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 Smatrices 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 oneparameter 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 AlekseevShatashvili 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.
Published as SciPost Phys. 11, 070 (2021)
Author comments upon resubmission
List of changes
 We added a comment in the discussion session about the analog formalism for JT gravity, as suggested by the referee.
 We corrected the typos and changed the definition of the hypersurface volume form in (3.13) so that (3.12) and (B.5) are consistent with it.