Turbulence on open string worldsheets under non-integrable boundary conditions

TL;DR

This paper investigates the turbulent behavior of open strings in AdS3 spacetime under different boundary conditions, revealing turbulence and non-integrability for fixed endpoints, and no turbulence for free endpoints.

Contribution

It demonstrates the emergence of turbulence in open strings with fixed endpoints in AdS3, indicating non-integrability, and confirms integrability when endpoints are free.

Findings

Turbulence observed with fixed boundary conditions.

No turbulence with free boundary conditions.

Non-integrability linked to fixed endpoints.

Abstract

We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.