Chaos of Wilson loop from string motion near black hole horizon

Abstract

To find the origin of chaos near the 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 a pure AdS background. The calculated Lyapunov exponent λ satisfies the universal bound λ≤2πTH for the Hawking temperature TH. 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 2πTH. Our work demonstrates that the black hole horizon is the origin of the chaos, and suggests a close interplay between chaos and quark deconfinement.