Quantum Chaos in Perturbative super-Yang-Mills Theory

TL;DR

This paper provides numerical evidence that the spectrum of anomalous dimensions in maximally supersymmetric SU(N) Yang-Mills theory exhibits chaos at finite N, with spectral properties aligning with random matrix theory predictions.

Contribution

It demonstrates that the perturbative spectrum transitions from integrable to chaotic behavior at finite N and extends analysis to two-loop order and deformations.

Findings

Finite N spectrum follows Wigner-Dyson distribution.

Spectral rigidity matches random matrix theory.

Eigenvectors display properties of chaotic states.

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.