{"paper":{"title":"Blowups in BPS/CFT correspondence, and Painlev\\'e VI","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.DG","math.MP"],"primary_cat":"hep-th","authors_text":"Nikita Nekrasov","submitted_at":"2020-07-07T17:33:54Z","abstract_excerpt":"We study four dimensional supersymmetric gauge theory in the presence of surface and point-like defects (blowups) and propose an identity relating partition functions at different values of $\\Omega$-deformation parameters $({\\varepsilon}_{1}, {\\varepsilon}_{2})$. As a consequence, we obtain the formula conjectured in 2012 by O$.$Gamayun, N$.$Iorgov, and O$.$Lysovyy, relating the tau-function ${\\tau}_{PVI}$ to $c=1$ conformal blocks of Liouville theory and propose its generalization for the case of Garnier-Schlesinger system. To this end we clarify the notion of the quasiclassical tau-function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.03646","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/2007.03646/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"}