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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
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
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
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 thank the referees for their reports and apologise for the long delay in the resubmission. We have attempted to make minor revisions to address the points raised by the referees. In particular:

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)

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