Chaos of Wilson Loop from String Motion near Black Hole Horizon

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 $\lambda \le 2\pi T_{\mathrm{H}}$ for the Hawking temperature $T_{\mathrm{H}}$. 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 $2\pi T_{\mathrm{H}}$. Our work demonstrates that the black hole horizon is the origin of the chaos, and suggests a close interplay between chaos and quark deconfinement.

12 pages, 7 figures

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• Turbulence on open string worldsheets under non-integrable boundary conditions
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