Many-body chaos and pole-skipping in holographic charged rotating fluids

TL;DR

This paper explores pole-skipping as a signature of quantum chaos in holographic charged rotating fluids, revealing how gauge choices affect energy-density fluctuations and analyzing butterfly velocity dependence on charge and rotation.

Contribution

It demonstrates the gauge dependence of energy-density fluctuation equations and clarifies conditions for pole-skipping in rotating charged black holes.

Findings

Discrepancy in near-horizon equations depends on gauge choice.

Proper boundary conditions eliminate gauge dependence.

Butterfly velocity varies with charge and rotation parameters.

Abstract

Recent developments identify pole-skipping as a `smoking-gun' signature of the hydrodynamic nature of chaos, offering an alternative way to probe quantum chaos in addition to the out-of-time-ordered correlator (OTOC). We study the quantum chaos and pole-skipping phenomenon in the strongly coupled charged rotating fluids, holographically dual to rotating black holes with nontrivial gauge field. We find that the near-horizon equation governing energy-density fluctuations differs from the source-less shock wave equation determining the OTOC, which depends on the $U(1)$ gauge choice. This discrepancy is eliminated under an appropriate boundary condition on the $U(1)$ gauge potential at the event horizon, as required by the vanishing of Wilson loop at the Euclidean horizon. We further investigate the dependence of the butterfly velocity on the charge and rotation parameters in a specific black hole configuration--the Cveti\v{c}-L\"u-Pope solution.