{"paper":{"title":"A simple formula for the $x$-$y$ symplectic transformation in topological recursion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP","math.OA","math.PR"],"primary_cat":"math-ph","authors_text":"Alexander Hock","submitted_at":"2022-11-16T13:55:46Z","abstract_excerpt":"Let $W_{g,n}$ be the correlators computed by Topological Recursion for some given spectral curve $(x,y)$ and $W^\\vee_{g,n}$ for $(y,x)$, where the role of $x,y$ is inverted. These two sets of correlators $W_{g,n}$ and $W^\\vee_{g,n}$ are related by the $x$-$y$ symplectic transformation. Bychkov, Dunin-Barkowski, Kazarian and Shadrin computed a functional relation between two slightly different sets of correlators. Together with Alexandrov, they proved that their functional relation is indeed the $x$-$y$ symplectic transformation in Topological Recursion. This article provides a fairly simple fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08917","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.08917/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}