SciPost Submission Page
3D Gravity in a Box
by Per Kraus, Ruben Monten, Richard M. Myers
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Per Kraus · Ruben Monten 
Submission information  

Preprint Link:  https://arxiv.org/abs/2103.13398v2 (pdf) 
Date submitted:  20210525 05:58 
Submitted by:  Monten, Ruben 
Submitted to:  SciPost Physics 
Ontological classification  

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.
Current status:
Reports on this Submission
Anonymous Report 1 on 2021821 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2103.13398v2, delivered 20210821, doi: 10.21468/SciPost.Report.3421
Strengths
1Makes very clear what the key findings are. The paper is selfcontained and pedagogical.
2Explains the origin of "statedependent conformal symmetry", which was always a puzzling aspect of the literature on $T\bar{T}$.
3The paper derives the AlekseevShatashvili symplectic form by working in metric variables.
4Concrete, detailed computations that pass consistency checks.
Weaknesses
1The magic of the solvability of the $T\bar{T}$ spectrum in field theory remains unexplained from the gravitational description.
Report
This paper is an important contribution to the holographic investigations of $T\bar{T}$deformed CFTs. It resolves a major confusion in the literature, where a structure appearing in these theories was interpreted as "statedependent conformal symmetry". The paper investigates this question systematically, and explains that the corresponding "charges" are not conserved, instead they are just some nice set of observables obeying a nontrivial rigid algebra. I expect that the formalism presented in this paper will be the starting point of any future investigation in this direction. The paper is very wellwritten and pedagogical, hence I recommend it for publication.
I have one question to the authors: Is the formalism adaptable to JT gravity? Could the program of the paper be carried out to all orders in this simpler theory? JT gravity has a twodimensional phase space, and in [31] very suggestive results were obtained about the relation between the cutoff JT theory and the $T\bar{T}$deformed Schwarzian theory.
Requested changes
1I found a couple of typos:
Both in (3.12) and above (B.5) the authors write $d^dx$ instead of $dx^d$. In sec. 6.4 they write "we now which to perform"
Author: Ruben Monten on 20210830 [id 1719]
(in reply to Report 1 on 20210821)We thank the referee for the very interesting suggestion and for pointing out the typos.
Regarding the typos: in the new version we have fixed the definition of the hypersurface volume form in (3.13) so that (3.12) and (B.5) are consistent with it.
As for the suggestion to apply this formalism to JT gravity at finite cutoff: indeed, we believe that it should apply. Moreover, given the explicit solutions in Section 2 of [31], it is conceivable that this program can be carried out to all orders in perturbation theory. We added a comment to this effect in the discussion section and hope to report on the results in a separate article in the future.