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arXiv · 1311.3241

On Marginal Deformations and Non-Integrability

Dimitrios Giataganas·Leopoldo A. Pando Zayas·Konstantinos Zoubos
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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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Dimitrios Giataganas, Leopoldo A. Pando Zayas, Konstantinos Zoubos. 2013-11-13. On Marginal Deformations and Non-Integrability. https://doi.org/10.1007/jhep01(2014)129

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