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Late time physics of holographic quantum chaos
by Alexander Altland, Julian Sonner
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Submission summary
| Authors (as registered SciPost users): | Julian Sonner |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2008.02271v2 (pdf) |
| Date submitted: | 2020-10-27 10:24 |
| Submitted by: | Sonner, Julian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy ${\cal O} \left(e^{-S} \right)$ with $S$ the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between "different universes" and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2021-1-18 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2008.02271v2, delivered 2021-01-18, doi: 10.21468/SciPost.Report.2428
Strengths
1-The statement is clear.
2. It is multidisciplinary that makes it useful for a wide range of people of interest.
Weaknesses
1- There are few typos should be fixed.
Report
This paper is devoted to study certain universal nature of chaotic spectral correlations within
a framework of an effective field theory with symmetry breaking pattern.
An interesting question people are trying to explore is to see in what extend having the disorder average or ensemble averaging is crucial in this context.
In this paper the authors have argued
that their approach is applicable for both system with and without ensembles or disorder averages.
The main role is played by what is called causal symmetry breaking.
I found the paper very interesting and promising though a little bit hard to read for people who are not expert in the filed.
This might be the case mainly because of the nature of the subject, being multidisciplinary.
I think the paper has interesting impact on the field and therefore I recommend its publication.
Report #1 by Anonymous (Referee 1) on 2021-1-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2008.02271v2, delivered 2021-01-12, doi: 10.21468/SciPost.Report.2396
Strengths
1- This paper very clearly reviews a formalism for understanding some universal behavior (statistics of energy levels) in chaotic quantum systems, with an emphasis on applications to quantum gravity. This formalism is not widely appreciated in the quantum gravity community, but is certainly of some interest to this community. Likewise, recent developments in this subject from the quantum gravity community may be of interest to the condensed matter/quantum chaos community, for whom the formalism described is more well known, but the applications to quantum gravity may not be. The paper does a good job of making the material accessible, and will likely be a valuable resource for researchers trying to understand progress made in the other field.
2- This paper also provides some novel applications of this formalism for 2D quantum gravity.
Weaknesses
1- Just a couple of very minor points/typos which I thought were unclear, which I list below.
Report
I think this is a very useful paper and worthy of being published in this journal.
Requested changes
1- The term "low energies" is sometimes used to mean small energy differences. While this is clarified on page 10, there are a couple of instances before this in which I think it might be unclear.
2- Throughout most of the paper the trace is denoted with lowercase tr, but on page 7 "Tr" is used.
3- In the figure near the top of page 16, I think some of the arrows might be facing the wrong direction.
4- A typo on page 17, second to last paragraph, it says "two two" instead of "to two".
5- On page 27, just below eq. 3.23, there are two epsilons when I think there should be one.
6- On page 31, in the last sentence of the caption for Figure 2, it says "s world-sheet" instead of "a world-sheet".