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Quantum Chaos in Perturbative super-Yang-Mills Theory
by Tristan McLoughlin, Raul Pereira, Anne Spiering
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Submission summary
Authors (as registered SciPost users): | Tristan McLoughlin |
Submission information | |
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Preprint Link: | scipost_202104_00019v1 (pdf) |
Date submitted: | April 16, 2021, 6:38 p.m. |
Submitted by: | McLoughlin, Tristan |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
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Approach: | Theoretical |
Abstract
We provide numerical evidence that the perturbative spectrum of anomalous dimensions in maximally supersymmetric SU(N) Yang-Mills theory is chaotic at finite values of N. We calculate the probability distribution of one-loop level spacings for subsectors of the theory and show that for large N it is given by the Poisson distribution of integrable models, while at finite values it is the Wigner-Dyson distribution of the Gaussian orthogonal ensemble random matrix theory. We extend these results to two-loop order and to a one-parameter family of deformations. We further study the spectral rigidity for these models and show that it is also well described by random matrix theory. Finally we demonstrate that the finite-N eigenvectors possess properties of chaotic states.
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Reports on this Submission
Report #2 by Chethan Krishnan (Referee 2) on 2021-7-22 (Invited Report)
- Cite as: Chethan Krishnan, Report on arXiv:scipost_202104_00019v1, delivered 2021-07-22, doi: 10.21468/SciPost.Report.3277
Report
I have some minor comments, which may improve the quality of the paper. But I leave it to the authors whether they decide to make these changes, the paper is publishable as it stands.
Firstly, the paper seems to be written in a letter format. This is fine for the most part, but since this is a paper which is more or less self-contained once one takes the dilatation operators presented in (4), (5) and (9) as a given, I think it may be beneficial to provide an introductory discussion on the dilatation operator. This will make the paper immediately accessible to a much wider audience than the integrability community. The discussion can be in a small appendix, something like page 6 of hep-th/0307015.
Also it may be useful to give some references that orient the present paper in the broader landscape of physics -- From the stringy side as opposed to the gauge theory side, the observation that integrability is lost due to chaos in some N=1 backgrounds (even at infinite N, but on the string worldsheet) has been noted by Basu and Pando Zayas in 1103.4107. Another curious paper that is loosely related is one by Craps et al. 1612.04334, they find that even in the weak coupling limit of the D1-D5 system, at large N, probes behave chaotically. Since the finite N discussions of the present paper can be viewed as a step towards black hole physics, these examples of chaos may be worth pointing out.
Report #1 by Robert de Mello Koch (Referee 1) on 2021-5-30 (Invited Report)
- Cite as: Robert de Mello Koch, Report on arXiv:scipost_202104_00019v1, delivered 2021-05-30, doi: 10.21468/SciPost.Report.2996
Report
While the spectrum of the planar dilatation operator is well studied, this paper points out a facinating new direction, clearly extending the existing literature in a highly non-trivial way. Indeed, some of the most interesting questions, motivated by holography, are naturally posed for the finite $N$ theory. This paper has developed an interesting set of finite $N$ questions that can be addressed numerically. In addition, the discovered links to random marix theory are compeling and interesting, although not entirely unexpected.
I thoroughly enjoyed reading this paper and am convinced of its value. For this reason I have recommended that it is accepted. I would however encourage the authors to state the dimension of the space that the dilatation operator acts on, in Figure captions. This would be an extremely useful piece of information for others wishing to reproduce the published results.