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On Marginal Deformations and Non-Integrability

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arxiv 1311.3241 v1 pith:MRXVTEB4 submitted 2013-11-13 hep-th nlin.CD

Dimitrios Giataganas , Leopoldo A. Pando Zayas , Konstantinos Zoubos This is my paper · ORCID
classification hep-thnlin.CD
keywords betacomplexdeformationnon-integrabilitygenericmarginalnon-integrableparameter
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abstract

We study the interplay between a particular marginal deformation of ${\cal N}=4$ super Yang-Mills theory, the $\beta$ deformation, and integrability in the holographic setting. Using modern methods of analytic non-integrability of Hamiltonian systems, we find that, when the $\beta$ parameter takes imaginary values, classical string trajectories on the dual background become non-integrable. We expect the same to be true for generic complex $\beta$ parameter. By exhibiting the Poincar\'e sections and phase space trajectories for the generic complex $\beta$ case, we provide numerical evidence of strong sensitivity to initial conditions. Our findings agree with expectations from weak coupling that the complex $\beta$ deformation is non-integrable and provide a rigorous argument beyond the trial and error approach to non-integrability.

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Cited by 4 Pith papers

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    For a warped AdS background with a GKP string vacuum, the author argues that the particle-side integrability constraint on the warp factor derivative g''(0) equals the worldsheet S-matrix factorization constraint on t...

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    hep-th 2024-11 conditional novelty 5.0 of 10

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