{
  "abstract": "To an oriented quiver with boundary $Γ$ and a compact connected Lie group $G$ we associate a Nahm-Kirchhoff moduli space $\\mathcal{M}_{\\mathbb{H}}(Γ)$: solutions of Nahm's equations on the edges with Kirchhoff matching at interior vertices, modulo boundary-trivial gauge transformations. For connected $Γ$, $\\mathcal{M}_{\\mathbb{H}}(Γ)$ is a smooth manifold of dimension $4(|E|-|Γ_{\\mathrm{int}}|)\\dim G$ with a hyperkähler structure arising as an infinite-dimensional hyperkähler quotient. Via a Kempf-Ness argument on the Cartan-Hadamard manifold $G_{\\mathbb{C}}/G$, we prove a quiver analogue of Donaldson's theorem identifying it with the complex-symplectic quotient $\\mathcal{M}_{\\mathbb{C}}(Γ)$ of the complex Nahm equations by the complexified gauge group. This quotient is independent of edge lengths and isomorphic to a finite-dimensional complex-symplectic quotient of $(T^*G_{\\mathbb{C}})^E$, while the hyperkähler metric depends on them: uniform rescaling acts by a homothety, and the transported metrics genuinely vary. By cutting and gluing, $Γ\\mapsto\\mathcal{M}_{\\mathbb{C}}(Γ)$ is a 2D TQFT valued in complex Hamiltonian manifolds, à la Moore-Tachikawa, whereas the hyperkähler refinement is not functorial on $\\mathbf{Cob}_2$: spines of a cylinder with different lengths give non-isomorphic spaces. Retaining lengths, these spaces form a metric field theory, a functor of non-unital monoidal categories from metric cobordisms to hyperkähler manifolds composed by hyperkähler reduction; over each cone of $M_{g,n}^{\\mathrm{trop}}$ they give a family with fixed complex-symplectic fibre and varying metric. Finally, harmonic gauge representatives converge as an internal edge collapses, and on a long edge with regular semisimple Higgs field the Kempf-Ness minimizer is exponentially confined near its centralizer; the limiting metrics are left open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03384",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohamed Moussadek Maiza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cc22vsntk9mj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03384",
  "fulltext_url": null,
  "id": "cc22vsntk9mj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03384",
  "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",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220459707",
  "pdf_url": "https://arxiv.org/pdf/2610.03384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cc22vsntk9mj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.03384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Nahm-Kirchhoff Moduli Spaces, Hyperkähler Quotient and 2D Field theories",
  "title_text": "Nahm-Kirchhoff Moduli Spaces, Hyperkähler Quotient and 2D Field theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/cc22vsntk9mj7",
  "venue": "arXiv",
  "versions": []
}