{"paper":{"title":"Equivariant K-theory and refined Vafa-Witten invariants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Richard P. Thomas","submitted_at":"2018-09-28T20:41:33Z","abstract_excerpt":"In [MT2] the Vafa-Witten theory of complex projective surfaces is lifted to oriented $\\mathbb C^*$-equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in $t^{1/2}$ invariant under $t^{1/2}\\leftrightarrow t^{-1/2}$ which specialise to numerical Vafa-Witten invariants at $t=1$. On the \"instanton branch\" the invariants give the virtual $\\chi_{-t}^{}$-genus refinement of G\\\"ottsche-Kool. Applying modularity to their calculations gives predictions for the contribution of the \"monopole branch\". We calculate some cases and find perfect agreement. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00078","kind":"arxiv","version":4},"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/1810.00078/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"}