Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}

TL;DR

This paper demonstrates that classical string configurations in AdS_5 x T^{1,1} exhibit chaos, providing evidence that these string backgrounds are non-integrable, which impacts the understanding of string dynamics in such geometries.

Contribution

The study shows that strings in AdS_5 x T^{1,1} are chaotic, conclusively ruling out integrability for these backgrounds through dynamical analysis.

Findings

Chaotic behavior observed in string configurations

Positive Lyapunov exponent indicates chaos

Analysis based on KAM theorem supports non-integrability

Abstract

We show that certain classical string configurations in AdS_5 x T^{1,1} are chaotic. This answers the question of integrability of string on such backgrounds in the negative. We consider a string localized in the center of AdS_5 that winds around two circles of T^{1,1}. The corresponding dynamical system is equivalent to two coupled gravitational pendula and allows a very intuitive understanding. We find conclusive evidence of chaotic behavior by systematically analyzing the workings of the KAM theorem. We also show that the largest Lyapunov exponent is positive.