{
  "abstract": "We provide the first mathematical construction of the non-Abelian Yang-Mills-Higgs measure on a two-dimensional torus by implementing Parisi and Wu's ``stochastic quantisation'' procedure. We use a specific gauge covariant (but non-Markovian) approximation to the previously constructed associated Langevin dynamics and develop a covariant paracontrolled calculus for it. This allows us to obtain short-time control over times that are much longer than what the cubic nonlinearity naïvely suggests. When combined with the decay properties of the Yang-Mills-Higgs action under the deterministic gradient flow, as well as a quantitative measure of how the noise pushes the dynamic away from Yang-Mills connections, this is good enough to yield uniform-in-time bounds. We finally show that there exists a renormalisation under which our gauge covariant approximation converges to the Langevin dynamics (modulo gauge transformation) and that the latter is topologically irreducible and strong Feller. It therefore admits a unique invariant measure, providing the sought-after construction. Our construction is non-perturbative and works in particular for any fixed values of the coupling constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03640",
  "author_total": 4,
  "authors": [
    {
      "name": "Bjoern Bringmann"
    },
    {
      "name": "Sky Cao"
    },
    {
      "name": "Martin Hairer"
    },
    {
      "name": "Wenhao Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qvbv41gzj2zs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03640",
  "fulltext_url": null,
  "id": "1qvbv41gzj2zs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03640",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03640",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qvbv41gzj2zs.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:04Z",
      "native_id": "2611.03640",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03640"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Construction of the 2D non-Abelian Yang-Mills-Higgs measure via stochastic quantisation",
  "title_text": "Construction of the 2D non-Abelian Yang-Mills-Higgs measure via stochastic quantisation",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/1qvbv41gzj2zs",
  "venue": "arXiv",
  "versions": []
}