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 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.

Chaos of QCD string from holography

“…This expression shows that a larger L q makes the chaos diminished. By this analytic expression (35), we can fit our numerical lower bound of the chaos, Fig. 8.…”

Chaos in a QQ¯ system at finite temperature and baryon density

“…As suggested in [20], a simple model suitable for an analytical treatment of the time-dependent perturbations is a square string in the AdS-RN background geometry (3), depicted in Fig. 3.…”

“…(1) using the AdS/CFT correspondence [11][12][13], adopting a dual geometry with a black hole and identifying T with the Hawking temperature, for example, in [14,15]. In particular, the heavy quark-antiquark pair, described holographically by a string hanging in the bulk with end points on the boundary [16][17][18][19], has been studied in this context [20][21][22]. For this system λ is the Lyapunov exponent characterizing the chaotic behavior of time-dependent fluctuations around the static configuration.…”

“…1). To investigate the onset of chaos for this system focusing on the effects of the chemical potential, we use the same approach adopted in [20] for the system at μ ¼ 0 to shed light on the differences with respect to the case of vanishing chemical potential.…”

Phase diagram of QCD chaos in linear sigma models and holography

“…Currently, it is known that quantum chaos plays a crucial role to characterize black holes in the AdS/CFT [6,7], and a maximal chaos is thought of as a criterion for a QFT to have a gravity dual [7][8][9][10]. The chaos index is a Lyapunov exponent defined through out-oftime-orderd correlators [8][9][10][11][12][13][14] in QFT, and corresponding exponent should be observed in chaotic motion of the fundamental string or D-branes in a curved spacetime [15][16][17][18][19][20][21]. A holographic study of chaos of meson condensate was provided in [1] for the supersymmetric D3/D7 model [2,22].…”