{"paper":{"title":"Yang-Baxter $\\sigma$-models, conformal twists, and noncommutative Yang-Mills theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP","nlin.SI"],"primary_cat":"hep-th","authors_text":"Eoin \\'O Colg\\'ain, Ilya Bakhmatov, Jun-ichi Sakamoto, Kentaroh Yoshida, Mohammad M. Sheikh-Jabbari, Thiago Araujo","submitted_at":"2017-02-09T15:30:21Z","abstract_excerpt":"The Yang-Baxter $\\sigma$-model is a systematic way to generate integrable deformations of AdS$_5\\times$S$^5$. We recast the deformations as seen by open strings, where the metric is undeformed AdS$_5\\times$S$^5$ with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter $\\Theta$. We identify the deformations of AdS$_5$ as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity conditon on $r$-matrices for supergravity solutions translates into $\\Theta$ being divergence-free. Integrabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02861","kind":"arxiv","version":2},"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"}