Turbulent strings in AdS/CFT

TL;DR

This paper investigates the nonlinear dynamics of flux tubes in a strongly coupled gauge theory via AdS/CFT, revealing cusp formation, turbulence, and force divergence in string oscillations.

Contribution

It introduces a detailed numerical analysis of string perturbations in AdS space, uncovering conditions for cusp formation and turbulence in the flux tube dynamics.

Findings

Cusps form on the string under certain perturbations.

Weak turbulence and power law energy spectra are observed.

Force divergence occurs when cusps reach the boundary.

Abstract

We study nonlinear dynamics of the flux tube between an external quark-antiquark pair in $\mathcal{N}=4$ super Yang-Mills theory using the AdS/CFT duality. In the gravity side, the flux tube is realized by a fundamental string whose endpoints are attached to the AdS boundary. We perturb the endpoints in various ways and numerically compute the time evolution of the nonlinearly oscillating string. As a result, cusps can form on the string, accompanied by weak turbulence and power law behavior in the energy spectrum. When cusps traveling on the string reach the boundary, we observe the divergence of the force between the quark and antiquark. Minimal amplitude of the perturbation below which cusps do not form is also investigated. No cusp formation is found when the string moves in all four AdS space directions, and in this case an inverse energy cascade follows a direct cascade.