Chaos of Wilson Loop from String Motion near Black Hole Horizon

TL;DR

This paper investigates the chaotic behavior of strings near black hole horizons within the AdS/CFT framework, revealing that the horizon induces chaos in Wilson loops and relates to quark deconfinement.

Contribution

It demonstrates that black hole horizons are the source of chaos in string dynamics and connects this chaos to thermal gauge theory phenomena, with numerical and analytical evidence.

Findings

Chaos is observed in string motion near black hole horizons.

Lyapunov exponent saturates the universal bound $oxed{ ext{lambda} \, \leq \, 2\pi T_H}$.

Horizon-related saddle points govern the chaotic behavior.

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.