Abstract
To find the origin of chaos near black hole horizon in string-theoretic AdS/CFT correspondence, we perform a chaos analysis of a suspended string in AdS black hole backgrounds. It has a definite CFT interpretation: chaos of Wilson loops, or in other words, sensitive time-evolution of a quark antiquark force in thermal gauge theories. Our nonlinear numerical simulation of the suspended Nambu-Goto string shows chaos, which would be absent in pure AdS background. The calculated Lyapunov exponent $\lambda$ satisfies the universal bound $\lambda \leq 2\pi T_{\rm H}$ for the Hawking temperature $T_{\rm H}$. We also analyze a toy model of a rectangular string probing the horizon and show that it contains a universal saddle characterized by the surface gravity $2\pi T_{\rm H}$. Our work demonstrates that the black hole horizon is the origin of the chaos, and suggests a close interplay between chaos and quark deconfinement.
Highlights
The renowned AdS=CFT correspondence [1] asserts that a certain class of quantum field theories allows a corresponding gravity description
We study the dynamics of the fundamental string in this geometry, in particular, when a part of the string is close to the black hole horizon r 1⁄4 rH
We argued that the Lyapunov exponent for a string moving in the near-horizon region takes a universal value that depends only on the horizon temperature
Summary
The renowned AdS=CFT correspondence [1] asserts that a certain class of quantum field theories allows a corresponding gravity description. In this paper we provide a concrete chaos analysis of motion of a fundamental string very near the black hole horizon. To study the origin of the chaos, we look at the solid thick line of the string in Fig. 1 since it probes very near the black hole horizon. This configuration has not been studied in the literature because it is not the minimum energy configuration. We find that the measured Lyapunov exponent satisfies the universal bound, λ ∼ 0.065 × 2πTH This is our prediction for the chaos of the interquark forces in thermal gauge theories with an AdS-Schwarzschild gravity dual. The last section is devoted to a summary and discussion of the interpretation of our Lyapunov exponents as a CFT out-of-time-order correlator
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