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Quantum chaos in 2D gravity

by Alexander Altland, Boris Post, Julian Sonner, Jeremy van der Heijden, Erik Verlinde

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Submission summary

Authors (as registered SciPost users): Julian Sonner
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-01-10
Date submitted: 2022-11-11 11:13
Submitted by: Sonner, Julian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


We present a quantitative and fully non-perturbative description of the ergodic phase of quantum chaos in the setting of two-dimensional gravity. To this end we describe the doubly non-perturbative completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavor-matrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits $\mathrm{U}(n|n)$ causal symmetry breaking and restoration. JT gravity and its 2D-gravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their {\it universe field theory}, the Kodaira-Spencer (KS) theory of gravity, does. After directly deriving the fMT from brane-antibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) D-brane vacua. We interpret our results in terms of an open-closed string duality between holomorphic Chern-Simons theory and its closed-string equivalent, the KS theory of gravity. Emphasis will be put on relating these geometric principles to the characteristic spectral correlations of the quantum ergodic phase.

Author comments upon resubmission

Dear editor-in-charge,

We thank the referees for their positive review and constructive criticism of our paper `Quantum chaos in 2D gravity', submitted to SciPost Physics on 2022-07-01.
The referees clearly showed an interest in our paper and a sharp eye for its possible improvements. After reading the referee reports and Editorial Recommendation, we have incorporated the suggestions made therein, resulting in this revised version of the article submission. We will now list the changes made compared to version 1, in response to both reports.

List of changes

The main revision to the article is a rewriting of the Introduction. As both referees have independently noted, the original introduction lacked clarity of presentation as well as a clear statement of the new results presented in this article. We believe that the new Introduction is more structured and unambiguously states the main aim, ideas and equations derived in the body of the work. Moreover, the original overview diagram (Figure 2 in the first version) has been replaced by a slimmed down diagram which highlights the principal connections made in the paper.

The other structural revision has been to combine all the reviewed material and necessary prior knowledge in a separate section, aptly titled 'Setting the scene'. The new material following this section has been made self-contained and more flowing. Moreover, some extra details of the computation are added where necessary. Lastly, a few minor typos were fixed and some references were added.

Published as SciPost Phys. 15, 064 (2023)

Reports on this Submission

Anonymous Report 2 on 2022-12-11 (Invited Report)


With these revisions the authors adressed my minor points of concern. Combining all background material in section 2 was an improvement in my opinion, and makes the paper more readable. I recommend the paper for publication.

  • validity: top
  • significance: good
  • originality: good
  • clarity: ok
  • formatting: perfect
  • grammar: perfect

Anonymous Report 1 on 2022-11-14 (Invited Report)


In the revised version the authors have substantially rewritten the introduction to better explain their results. This change was necessary; the paper assumes knowledge of the Kodaira-Spenser theory. Current version is much more accessible to a general reader, and conveys the logic of the main results quite well. I think the paper is ready to be accepted for publication.

  • validity: high
  • significance: good
  • originality: high
  • clarity: good
  • formatting: excellent
  • grammar: excellent

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