{
  "abstract": "The Nekrasov instanton partition function of the 4d $N=2^*$ U(N) gauge theory (a mass deformation of 4d $N=4$ 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 $q$. This note proves convergence of the series in the unit disk $|q|<1$ 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 $b^2=\\epsilon_1/\\epsilon_2$ of equivariant parameters is in $\\mathbb{C}\\setminus[0,+\\infty)$, the radius is 1, as expected. If $b^2$ is non-negative, three cases arise: the radius is finite if $b^2$ has finite exponential type (a generalization of Brjuno numbers), namely there exists $C>0$ such that $|b^2-p/q|>\\exp(-Cq)$ for all integers $p,q\\neq 0$; the series diverges if $b^2$ is super-exponentially well approximable by rationals; and if $b^2$ is rational some terms are singular. The AGT correspondence translates these results to convergence of torus one-point conformal blocks of the Virasoro and $W_N$ algebras with non-real $b$, within the unit disk. For the Virasoro algebra this corresponds to a central charge in $\\mathbb{C}\\setminus[25,+\\infty)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2602.19425",
  "author_total": 1,
  "authors": [
    {
      "name": "Bruno Le Floch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0n3xezx1wsdk0.bib",
  "cited_by": 1,
  "doi": "10.21468/scipostphyscore.9.2.038",
  "fulltext_url": null,
  "id": "0n3xezx1wsdk0",
  "issns": [
    "2666-9366"
  ],
  "landing_url": "https://hal.science/hal-05848469v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.hthe"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7165931814",
  "pdf_url": "https://hal.science/hal-05848469/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-25",
  "publisher": "SciPost Foundation",
  "ris": "https://research.draconitic.com/paper/0n3xezx1wsdk0.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:17Z",
      "native_id": "hal-05848469",
      "source": "hal",
      "url": "https://hal.science/hal-05848469v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "hal:1.phys.hthe",
      "subfield": "high-energy"
    }
  ],
  "title": "Convergence of Nekrasov instanton sum with adjoint matter",
  "title_text": "Convergence of Nekrasov instanton sum with adjoint matter",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T12:20:48Z",
  "url": "https://research.draconitic.com/paper/0n3xezx1wsdk0",
  "venue": "SciPost Physics Core",
  "versions": []
}