Abstract
We study the interplay between a particular marginal deformation of \( \mathcal{N} \) = 4 super Yang-Mills theory, the β deformation, and integrability in the holographic setting. Using modern methods of analytic non-integrability of Hamiltonian systems, we find that, when the β parameter takes imaginary values, classical string trajectories on the dual background become non-integrable. We expect the same to be true for generic complex β parameter. By exhibiting the Poincaré sections and phase space trajectories for the generic complex β case, we provide numerical evidence of strong sensitivity to initial conditions. Our findings agree with expectations from weak coupling that the complex β deformation is non-integrable and provide a rigorous argument beyond the trial and error approach to non-integrability.
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Giataganas, D., Zayas, L.A.P. & Zoubos, K. On marginal deformations and non-integrability. J. High Energ. Phys. 2014, 129 (2014). https://doi.org/10.1007/JHEP01(2014)129
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DOI: https://doi.org/10.1007/JHEP01(2014)129