Giataganas, DimitriosZayas, Leopoldo A. PandoZoubos, Konstantinos2015-07-212015-07-212014-01Giataganas D, Zayas LAP & Zoubos K 2014, 'On marginal deformations and non-integrability', Journal of High Energy Physics, vol. 129, no.1, pp.1-16.1126-6708 (print)1029-8479 (online)10.1007/JHEP01(2014)129http://hdl.handle.net/2263/49121We study the interplay between a particular marginal deformation of 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 Poincar´e 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.en© 2014 Giataganas et al. ; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).AdS-CFT correspondenceConformal field models in string theoryArticle