{
  "abstract": "We study correlation functions of topologically twisted $\\mathcal N=2$ supersymmetric QCD with gauge group $\\mathrm{SU}(N)$ on a compact four-manifold $X$. We derive the Coulomb branch integral for all $N$, including new couplings to background fluxes for the flavor symmetry. For $X$ of simple type with $b_2^+>1$, the correlators become sums over a finite number of strong-coupling singularities on the Coulomb branch, and can be expressed using a number of Coulomb branch couplings. The sum contains the $\\mathcal N=1$ vacua, which become the supersymmetric vacua when the $\\mathcal N=2$ theory is broken to $\\mathcal N=1$ by an adjoint mass deformation, and whose contribution we attribute to the instanton branch. We focus on asymptotically free $\\mathrm{SU}(N)$ QCD with $N_f<2N$ equal mass hypermultiplets, and conjecture that its instanton contribution to topological correlators agrees with the generating function of virtual Segre numbers of rank $N$, which are intersection numbers on the moduli space of semistable sheaves on an algebraic surface. We present a precise dictionary for all $N$ between universal series for Segre numbers and Coulomb branch couplings at the $\\mathcal N=1$ vacua. The calculation of these couplings requires new higher-rank techniques, involving Siegel modular forms, an exact $\\mathbb Z_N$ symmetry, charge conjugation symmetry, factorisation of the Seiberg--Witten curve, and the blowup formula. For pure $\\mathrm{SU}(N)$, our result agrees with earlier work by Mariño and Moore, and the twisted correlators give the $\\mathrm{SU}(N)$ Donaldson invariants of $X$. For $\\mathrm{SU}(3)$ QCD, we determine closed-form expressions for all 13 Coulomb branch couplings for each $N_f=1,\\dots, 5$, and find precise agreement with results of Göttsche and Kool for virtual rank 3 Segre numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03874",
  "author_total": 2,
  "authors": [
    {
      "name": "Elias Furrer"
    },
    {
      "name": "Ranveer Kumar Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5w7mmn17aypz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03874",
  "fulltext_url": null,
  "id": "5w7mmn17aypz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03874",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7220723743",
  "pdf_url": "https://arxiv.org/pdf/2610.03874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5w7mmn17aypz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.03874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "SU($N$) QCD, four-manifolds and Segre numbers",
  "title_text": "SU(N) QCD, four-manifolds and Segre numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/5w7mmn17aypz9",
  "venue": "arXiv",
  "versions": []
}