Chaos rules out integrability of strings on AdS5×T1,1

We show that certain classical string configurations in AdS5×T1,1 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 AdS5 that winds around two circles of T1,1. 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.