Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantum Chaos in Topologically Massive Gravity

Yan Liu, Avinash Raju

Abstract

We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.

Quantum Chaos in Topologically Massive Gravity

Abstract

We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.

Paper Structure

This paper contains 20 sections, 84 equations, 1 figure.

Table of Contents

  1. Introduction
  2. BTZ black holes : a short review
  3. Quantum chaos in Einstein gravity
  4. Euclidean two-point correlator from holography
  5. Retarded Green's function from CFT
  6. Quantum chaos in topologically massive gravity
  7. Out-of-time-order correlator from shock waves
  8. High temperature limit of instantaneous Lyapunov exponents
  9. Lyapunov Exponents and Butterfly Velocities from OTOC
  10. OTOC at the chiral point $\mu=1$
  11. Pole-skipping from near horizon
  12. Pole-skipping from holographic massive mode
  13. Pole-skipping from CFT analysis
  14. Conclusion and Discussions
  15. BTZ in Different Coordinates
  16. ...and 5 more sections

Figures (1)

  • Figure 1: The plot shows the numerical fitting for pole-skipping $\text{Im} \omega$ (blue) and $\text{Im} k$ (orange) as a function of $\delta$. The solid lines corresponds to the analytic curve $(\text{Im} \omega, \text{Im} k) = (2,2(1+2\delta))$ while the dots are our numerical results for various $\delta$.