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Disorder in AdS$_3$/CFT$_2$

by Moritz Dorband, Daniel Grumiller, René Meyer, Suting Zhao

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Submission summary

Authors (as registered SciPost users): Moritz Dorband · Daniel Grumiller · Rene Meyer
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-12-27
Date submitted: 2023-11-28 16:52
Submitted by: Dorband, Moritz
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We perturbatively study marginally relevant quenched disorder in AdS$_3$/CFT$_2$ to second order in the disorder strength. Using the Chern-Simons formulation of AdS$_3$ gravity for the Poincar\'e patch, we introduce disorder via the chemical potentials. We discuss the bulk and boundary properties resulting from the disorder averaged metric. The disorder generates a small mass and angular momentum. In the bulk and the boundary, we find unphysical features due to the disorder average. Motivated by these features, we propose a Poincar\'e-Lindstedt-inspired resummation method. We discuss how this method enables us to remove all of the unphysical features and compare with other approaches to averaging.

Author comments upon resubmission

Dear Editor,
We thank the referee for their additional comments and questions, which we addressed in our last edition of the paper. Below we address the comments of the report dated Nov.01.2023 and the corresponding changes in our manuscript. A list of all changes of our manuscript is given after our answers to the referees comments.

To better highlight the issue addressed by the main question of the referee, we added a statement at the end of our abstract and included a new subsection 5.2 where we discuss this important issue raised by the referee. We summarize the essence of this discussion already in a new paragraph at the end of the introduction (before the organization of the paper), which we quote here:

''Finally, we compare our results with those obtained by first calculating observables for each realisation of the disorder and then averaging only the final result. In particular, we obtain an averaged energy-momentum tensor that differs from the one generated through the Poincaré-Lindstedt-inspired method. The main disadvantage of this, otherwise straightforward, alternative is that there is no way to associate an effective metric with the resulting energy-momentum tensor. In particular, the averaged boundary metric does not provide a source for the averaged boundary energy-momentum tensor.''
Moreover, we also added a brief summary of these statements in the concluding section 6 at the end of p. 20/beginning of p. 21.

We refer now to appendix D in the beginning of section 5 and in the paragraph ''Beyond perturbation theory'' on p. 21.

With best regards,
M. Dorband, D. Grumiller, R. Meyer and S. Zhao

List of changes

- added half-sentence at the end of the abstract: ''and compare with other approaches to averaging.''
- added a paragraph on the new subsection 5.2 on the upper half of p. 5: ''Finally, we compare ... energy-momentum tensor.''
- at the end of the introduction, added one sentence referring to to sec. 5.2: ''In the second part ... the final result.''
- restructured previous section 5; content of old section 5 is now subsection 5.1, added new subsection 5.2 on p. 18-19
- added a paragraph in the conclusion at the bottom of p. 20 concerning the new subsection 5.2: ''Furthermore, as discussed ... energy-momentum tensor eq. (79).''
- added a reference to appendix D in the paragraph ''Beyond perturbation theory'' on p. 21
- corrected an overall sign typo in appendix A, eq. (85b)
- remade the plots in fig. 2 to account for the typo (typo did not affect the qualitative statements on the plots, as well as the other results discussed in the manuscript)

Published as SciPost Phys. 16, 017 (2024)

Reports on this Submission

Anonymous Report 1 on 2023-12-19 (Invited Report)


I would like to thank the authors for their effort in clarifying the issue I raised in my last report. I find the results in the new section 5.2 quite interesting and am also happy with the related changes in other parts of the manuscript. (I find it curious that the energy momentum tensor resulting from averaging over realizations vanishes for the case epsilon = \bar epsilon)
I am therefore satisfied with the current version of the article and recommend it for publication in this journal.

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