Chaos and pole-skipping in a simply spinning plasma

TL;DR

This paper explores the connection between quantum chaos and energy dynamics in a spinning plasma using holographic duality, providing new analytic results on pole-skipping phenomena and chaos indicators in rotating black hole backgrounds.

Contribution

It offers a general proof of pole-skipping in energy density correlators for rotating black holes and derives explicit relations between chaos parameters and pole-skipping points.

Findings

Pole-skipping occurs in the energy density Green's function for rotating black holes.

Analytic expression for OTOC on Hopf circles in the large black hole limit.

Lyapunov exponent and butterfly velocity relate to pole-skipping locations and are valid for any rotation.

Abstract

We study the relationship between many-body quantum chaos and energy dynamics in holographic quantum field theory states dual to the simply-spinning Myers-Perry-AdS$_5$ black hole. The enhanced symmetry of such black holes allows us to provide a thorough examination of the phenomenon of pole-skipping, that is significantly simpler than a previous analysis of quantum field theory states dual to the Kerr-AdS$_4$ solution. In particular we give a general proof of pole-skipping in the retarded energy density Green's function of the dual quantum field theory whenever the spatial profile of energy fluctuations satisfies the shockwave equation governing the form of the OTOC. Furthermore, in the large black hole limit we are able to obtain a simple analytic expression for the OTOC for operator configurations on Hopf circles, and demonstrate that the associated Lyapunov exponent and butterfly velocity are robustly related to the locations of a family of pole-skipping points in the energy response. Finally, we note that in contrast to previous studies, our results are valid for any value of rotation and we are able to numerically demonstrate that the dispersion relations of sound modes in the energy response explicitly pass through our pole-skipping locations.