Scrambling or Stalling: Angular Momentum Barriers to Chaos in Holographic CFTs

TL;DR

This paper investigates how angular momentum barriers affect the scrambling process in high-temperature holographic CFTs, revealing conditions under which chaos is delayed or halted due to bulk particle dynamics.

Contribution

It provides an analytic relation between scrambling times and particle kinematics in BTZ and AdS-Schwarzschild geometries, and extends the analysis to higher dimensions showing the impact of angular momentum barriers.

Findings

Scrambling times are linked to particle trajectories in the bulk.

Angular momentum barriers can halt or slow down scrambling.

Analytic expressions match CFT computations for 2D cases.

Abstract

Scrambling is a diagnostic of quantum chaos in strongly coupled systems, and plays a central role in the holographic description of black hole dynamics. We study scrambling in high-temperature holographic CFTs, with an emphasis on perturbations dual to particles on infalling and bound trajectories in the bulk description. For BTZ and AdS-Schwarzschild geometries, we derive an analytic expression relating the difference in scrambling times to the particles' kinematics. We match this to a 2d CFT computation by constructing the smeared operator that creates the bulk particle with the desired kinematics and calculating the out-of-time-ordered correlator (OTOC). For higher-dimensional holographic CFTs, the scrambling slows and eventually ceases when the dual bulk particle has insufficient energy to overcome the angular momentum barrier.