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

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

2011-03-21

arxiv.org/abs/1103.4107v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 11 figures

Scientific paper

10.1016/j.physletb.2011.04.063

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.

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