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arXiv · 1103.4101

Integrability Lost

Pallab Basu·Diptarka Das·Archisman Ghosh
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Abstract

It is known that classical string dynamics in pure AdS_5\times S^5 is integrable and plays an important role in solvability. This is a deep and central issue in holography. Here we investigate similar classical integrability for a more realistic confining background and provide a negative answer. The dynamics of a class of simple string configurations in AdS soliton background can be mapped to the dynamics of a set of non-linearly coupled oscillators. In a suitable limit of small fluctuations we discuss a quasi-periodic analytic solution of the system. However numerics indicates chaotic behavior as the fluctuations are not small. Integrability implies the existence of a regular foliation of the phase space by invariant manifolds. Our numerics shows how this nice foliation structure is eventually lost due to chaotic motion. We also verify a positive Lyapunov index for chaotic orbits. Our dynamics is roughly similar to other known non-integrable coupled oscillators systems like Henon-Heiles equations.

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Pallab Basu, Diptarka Das, Archisman Ghosh. 2011-06-13. Integrability Lost. https://doi.org/10.1016/j.physletb.2011.04.027

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