{"paper":{"title":"Convergence of Nekrasov instanton sum with adjoint matter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Bruno Le Floch","submitted_at":"2026-02-23T01:44:19Z","abstract_excerpt":"The Nekrasov instanton partition function of the 4d $\\mathcal{N}=2^*$ $U(N)$ gauge theory (a mass deformation of 4d $\\mathcal{N}=4$ super-Yang-Mills theory), which is a generating series of equivariant integrals over instanton moduli spaces, is given by a sum over colored partitions weighted by a counting parameter $\\mathfrak{q}$. This note proves convergence of the series in the unit disk $|\\mathfrak{q}|<1$ for generic parameters. Specifically, the absolute convergence radius of this sum is determined, assuming that mass and Coulomb branch parameters avoid some lattice. If the ratio $b^2=\\eps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.19425","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/2602.19425/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"}