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Quantum Chaos in Perturbative super-Yang-Mills Theory
by Tristan McLoughlin, Raul Pereira, Anne Spiering
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Tristan McLoughlin |
| Submission information | |
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| Preprint Link: | scipost_202104_00019v2 (pdf) |
| Date accepted: | 2022-10-03 |
| Date submitted: | 2022-08-30 14:54 |
| Submitted by: | McLoughlin, Tristan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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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.
Author comments upon resubmission
We have extended the introduction to N=4 SYM in section 2.1 giving some further details about the action of the symmetry generators and the dilatation operator in particular. We have added the references to Basu and Pando-Zayas (and an earlier work by Pando Zayas and Terrero-Escalante) to our discussion chaotic string worldsheet theories. We have added a brief comment on the work by Balasubramanian et al.
Following the second referees suggestion we have added the number of states i.e. the dimension of the Hilbert space to all our figures.
Published as SciPost Phys. 14, 049 (2023)