Chaos in M(atrix) Theory

TL;DR

This paper investigates chaos in M(atrix) theory, demonstrating classical chaos, exploring quantum chaos features, and discussing implications for holography and supersymmetric Yang-Mills theory.

Contribution

It shows classical chaos in M(atrix) theory and links quantum chaotic energy eigenvalues to holographic properties, also analyzing supersymmetric Yang-Mills dynamics.

Findings

Classical trajectories in M(atrix) theory are chaotic.

Quantum energy eigenvalues exhibit repulsive features linked to chaos.

Slow modes contribute singularly to fast mode Hamiltonian.

Abstract

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive feature of energy eigenvalues in quantum chaotic system. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed. We demonstrate that after the separation of "slow" and "fast" modes there is a singular contribution from the "slow" modes to the Hamiltonian of the "fast" modes.