{"paper":{"title":"The Dilatation Operator of $\\cal N$ $=$ 4 SYM and Classical Limits of Spin Chains and Matrix Models","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Abhishek Agarwal, Sarada.G.Rajeev","submitted_at":"2004-05-12T19:49:57Z","abstract_excerpt":"A study of the one loop dilatation operator in the scalar sector of $\\cal N$ $=$ 4 SYM is presented. The dilatation operator is analyzed from the point of view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in the planar large $N$ limit is presented, and its role in understanding the integrability of the planar dilatation operator is emphasized. A classical limit of the dilatation operator is obtained by considering a contraction of this Lie algebra, leading to a new way of constructing classical limits for quantum spin chains. An infinite tower of local conserved charg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0405116","kind":"arxiv","version":3},"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"}