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3D Gravity in a Box
by Per Kraus, Ruben Monten, Richard M. Myers
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Submission summary
| Authors (as registered SciPost users): | Per Kraus · Ruben Monten |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2103.13398v2 (pdf) |
| Date submitted: | 2021-05-25 05:58 |
| Submitted by: | Monten, Ruben |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| 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 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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2021-8-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2103.13398v2, delivered 2021-08-21, doi: 10.21468/SciPost.Report.3421
Strengths
1-Makes very clear what the key findings are. The paper is self-contained and pedagogical.
2-Explains the origin of "state-dependent conformal symmetry", which was always a puzzling aspect of the literature on $T\bar{T}$.
3-The paper derives the Alekseev-Shatashvili symplectic form by working in metric variables.
4-Concrete, detailed computations that pass consistency checks.
Weaknesses
1-The 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 "state-dependent 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 well-written 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 two-dimensional 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
1-I 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 2021-08-30 [id 1719]
(in reply to Report 1 on 2021-08-21)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.