Chaos of QCD string from holography

Abstract

It is challenging to quantify chaos of QCD, because nonperturbative QCD accompanies nonlocal observables. By using holography, we find that QCD strings at large ${N}_{c}$ and strong coupling limit exhibit chaos, and measure their Lyapunov exponent at zero temperature. A pair of a quark and an antiquark separated by ${L}_{q}$ in the large ${N}_{c}$ QCD is dual to a Nambu-Goto string hanging from the spatial boundary of the D4-soliton geometry. We numerically solve the motion of the string after putting a pulse force on its boundaries. The chaos is observed for the amplitude of the force larger than a certain lower bound. The bound increases as ${L}_{q}$ grows, and its dependence is well approximated by a hypothesis that the chaos originates in the endpoints of the QCD string.