{"paper":{"title":"On Marginal Deformations and Non-Integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"hep-th","authors_text":"Dimitrios Giataganas, Konstantinos Zoubos, Leopoldo A. Pando Zayas","submitted_at":"2013-11-13T18:27:46Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3241","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}