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

TL;DR

This work investigates quantum chaos in holographic CFTs dual to charged rotating black holes by connecting pole-skipping and OTOC analyses. Using five-dimensional Einstein-Maxwell-Chern-Simons theory and the CLP black hole, the authors show that a naive near-horizon energy-density equation is gauge-dependent and does not trivially match the pole-skipping condition, but imposing a physically motivated horizon boundary condition from the Wilson loop fixes the gauge and restores equivalence between the two chaos probes. They derive the pole-skipping point at $\omega=i2\pi T$ and compute the corresponding butterfly velocities both from pole-skipping and shock-wave methods, confirming their agreement for rotating, charged backgrounds. In the explicit CLP example, charge and rotation jointly shape the scrambling dynamics, with $v_B^+$ increasing toward the speed of light as rotation grows and $v_B^-$ crossing from negative to positive values, shifted by the charge; these results underscore the central role of horizon physics in holographic chaos and extend the pole-skipping–OTOC correspondence to more general, matter-filled spacetimes.

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 Cvetič-Lü-Pope solution.

Figures (2)

• Figure 1: Left: Butterfly velocity $v_B^\pm$ of \ref{['eq:butterfly']} as a function of the rotation parameter $a$ for the CLP solution with $q=1250$ (blue curve) and for the Myers-Perry-AdS$_5$ (red curve). Right: Butterfly velocity $v_B^\pm$ as a function of the charge parameter $q$ for the CLP solution with $a=0.4$ (bule curve) and for the RN-AdS (yellow curve). In both polts, dotted markers correspond to the $"+"$ sector of $v_B$, while triangle markers correspond to the $"-"$ sector. The gray dashed lines indicate the speed of light. The large black hole limit is ensured by setting $r_h=10,\, L=1$.
• Figure 2: The purple curve shows the root $a_0$ of $v_B^-=0$ as a function of $q$ for the CLP black hole, while the dashed line corresponds to that of the Myers-Perry-AdS$_5$ black hole with $a_0=\sqrt{2/3}$. We have set $r_h=10, L=1$.