Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
arXiv:1103.4107 · doi:10.1016/j.physletb.2011.04.063
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.
12 pages, 11 figures