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

Juan Hernandez, Andrew Rolph

TL;DR

This work links bulk angular-momentum barriers to chaos with boundary operator dynamics in holographic CFTs. By analyzing infalling and bound bulk particle trajectories, it derives analytic scrambling-time relations in BTZ and AdS-Schwarzschild and matches them to a 2d CFT OTOC computed from smeared boundary operators. A key finding is that scrambling slows and can cease as angular momentum approaches a critical value J_crit in higher dimensions, while in 2d the OTOC reproduces the expected Lyapunov behavior and a kernel-dependent shift of the butterfly cone. The results illuminate how bulk kinematics map to boundary operator growth, and they predict distinct high-dimensional chaotic vs quasi-integrable sectors with potential finite-N corrections and richer dynamics beyond the planar BTZ case.

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.

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

TL;DR

This work links bulk angular-momentum barriers to chaos with boundary operator dynamics in holographic CFTs. By analyzing infalling and bound bulk particle trajectories, it derives analytic scrambling-time relations in BTZ and AdS-Schwarzschild and matches them to a 2d CFT OTOC computed from smeared boundary operators. A key finding is that scrambling slows and can cease as angular momentum approaches a critical value J_crit in higher dimensions, while in 2d the OTOC reproduces the expected Lyapunov behavior and a kernel-dependent shift of the butterfly cone. The results illuminate how bulk kinematics map to boundary operator growth, and they predict distinct high-dimensional chaotic vs quasi-integrable sectors with potential finite-N corrections and richer dynamics beyond the planar BTZ case.

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.

Paper Structure

This paper contains 24 sections, 126 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Bulk calculation of the scrambling time
  3. Geometry and geodesics
  4. BTZ
  5. AdS-Schwarzschild
  6. Particle stress tensor
  7. Backreaction and the shockwave geometry
  8. Correlation function and scrambling time
  9. The CFT dual to inserting bulk particles
  10. Bulk particle wavepackets and smeared boundary operators.
  11. What is a particle?
  12. From bulk particle to boundary operator
  13. How to smear a boundary operator to give bulk particles boundary-parallel momentum
  14. CFT$_2$ calculation of the OTOC
  15. OTOC of local operators
  16. ...and 9 more sections

Figures (2)

  • Figure 1: We release a $W$-particle with some energy and angular momentum from near the AdS$_R$ boundary. This leads to a shockwave backreaction near the black hole horizon, and scrambling of the $W$-perturbation, as quantified by the $\bra{\text{TFD}}W_R V_L V_R W_R \ket{\text{TFD}}$ correlator. The scrambling time depends on the energy and momentum of the $W$-particle and the relative positions of the operators. The diagram on the right is the $t=0$ slice of the left-hand bulk's geometry, with the blue triangle representing the growing near-horizon shockwave.
  • Figure 2: A plot of $\Delta t_*$, Eq. \ref{['eq:deltat4']}, as a function of $P_x / E$ and for different values of $(x_{ V} - x_{ W})$. The curves overlap for negative values of $P_x/E$.