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JT gravity at finite cutoff
by Luca V. Iliesiu, Jorrit Kruthoff, Gustavo J. Turiaci, Herman Verlinde
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Submission summary
| Authors (as registered SciPost users): | Jorrit Kruthoff |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202006_00046v1 (pdf) |
| Date submitted: | 2020-06-15 02:00 |
| Submitted by: | Kruthoff, Jorrit |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We compute the partition function of 2D Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wavefunctional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering. In the second approach we perform the path integral exactly when summing over surfaces with disk topology, to all orders in perturbation theory in the cutoff. Both results precisely match the recently derived partition function in the Schwarzian theory deformed by an operator analogous to the $T\overline{T}$ deformation in 2D CFTs. This equality can be seen as concrete evidence for the proposed holographic interpretation of the $T\overline{T}$ deformation as the movement of the AdS boundary to a finite radial distance in the bulk.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2020-8-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202006_00046v1, delivered 2020-08-02, doi: 10.21468/SciPost.Report.1875
Strengths
1-originality
2-importance of the results
Report
This paper concerns the study of the finite cut-off partition function of 2D Jackiw-Teitelboim gravity.
Two different methods are adopted; an exact evaluation of the functional Wheeler-DeWitt wave in radial quantization and the direct computation of the Euclidean path integral.
Both techniques lead to results which precisely match the partition function in the Schwarzian theory deformed by the 1D analogue of the TTbar deformation of 2D CFTs. The paper is very well written and addresses critical issues related to the interpretation of the TTbar deformation within the AdS/CFT framework.
The main result corresponds to the chain of equalities (1.12). Section 4 is particularly inspiring as two different types of non-perturbing corrections to the partition function are discussed.
The presence, in the partition function, of contributions coming from the "contracting branch" is fascinating and it will undoubtedly trigger further work.
In conclusion, this is an excellent piece of work that contains many original comments and opens the discussion on many challenging questions. I have no hesitation in recommending this document for publication.
Requested changes
1- After eq. B1: seperation ->separation
Report #2 by Anonymous (Referee 2) on 2020-7-20 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202006_00046v1, delivered 2020-07-20, doi: 10.21468/SciPost.Report.1840
Strengths
1. Two concrete and detailed calculations of the bulk wavefunction/partition function are provided and matched with a previously existing boundary proposal, with many subtleties clearly elaborated.
2. A novel proposal for fixing the complex energy levels of TTbar-deformed theories is provided.
Report
This paper is a wonderful addition to the TTbar literature and provides the first quantum-mechanical check of the "1d TTbar deformation" = "finite cutoff AdS2" proposal, by matching formulas derived from a Dirichlet cutoff bulk to previously derived formulas in the boundary theory. Several complementary issues are discussed, with a potential fix to the complexification of energy levels being a particularly important one.
Something that is not addressed is the connection to mixed boundary conditions at the usual AdS boundary, as detailed by Guica and Monten. There, the equivalence between TTbar deformations and Dirichlet conditions at finite cutoff in AdS was shown to be true classically (and expected to differ quantum mechanically), while the results of this paper suggest the two are equivalent even quantum mechanically. Is there an explanation of this seeming discrepancy?
Report #1 by Anonymous (Referee 1) on 2020-7-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202006_00046v1, delivered 2020-07-10, doi: 10.21468/SciPost.Report.1816
Report
This is a remarkable paper addressing issues about imposing a finite-cutoff in the JT gravity in a finite-cutoff setup. They compare the methods from the evaluation of the Wheeler-DeWitt functional and the gravitational path integral in the bulk, obtaining agreement in the boundary.
This paper illustrates new perspectives among JT gravity, TTbar deformation, and the information paradox setup discussed recently in the high energy theory community.
A particularly important problem related to this story, and I am particularly interested in is the possible finiteness of entanglement entropy in the holographic cutoff AdS in higher dimensions. The problem appears in higher dimensions, but I am curious if this also emerges in this 1+1 dimensional bulk, and I believe that this might also be related to the information problem in the setup of JT gravity. I look forward to the authors' comments on it.