{"paper":{"title":"Instantons on the Blown-up Surface and the Affine Vertex Algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.RT"],"primary_cat":"math.AG","authors_text":"Qingyuan Jiang, Wei-ping Li, Yu Zhao","submitted_at":"2025-11-24T10:20:45Z","abstract_excerpt":"We answer a long-standing question raised by Vafa--Witten on a relation between S-duality and conformal field theory, which related Yoshioka's blow-up formula and the WZW model for $\\mathrm{SU}(r)$ at level $1$. Precisely, for the moduli space of Euler characteristics of rank $r$ instantons on the blow-up of an algebraic surface along a closed point, we construct the affine $\\mathrm{gl}_r$-action on various cohomology theories, including the Grothendieck group of coherent sheaves, Hochschild homology groups, Chow groups and Hodge cohomology groups, and identifying the module as a basic represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.18959","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.18959/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"}