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

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.

arXiv comment12 pages, 11 figures

References in corpus (15)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Aspects of Semiclassical Strings in AdS${}_5$
• Deformations of N=4 SYM and integrable spin chain models
• PP Wave Limit and Enhanced Supersymmetry in Gauge Theories
• On Penrose Limits and Gauge Theories
• Penrose Limit of N=1 Gauge Theories
• Chaos in the Gauge/Gravity Correspondence
• Integrability Lost
• Multi-spin strings on AdS(5)xT(1,1) and operators of N=1 superconformal theory
• Spinning Strings on Deformed AdS_5 x T^{1,1} with NS B-field
• Light-like Wilson Loops and Cusp Anomalous Dimensions in Non-conformal Gauge Theories

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