{
  "abstract": "In the Wilson formulation of lattice gauge theory, the fundamental degrees of freedom are group-valued link variables, while the action is a sum over the trace of the plaquettes, the smallest Wilson loops. For generative sampling methods such as normalizing flows, this poses a challenge: the distribution of an individual plaquette is easy to model, but mapping sampled plaquettes to the links is the obstruction. We explore a statistical way around this in two dimensions for the $\\mathrm{SU}(N)$ gauge theory with the Wilson plaquette action. The action can be written in terms of holonomy variables, which determine the links once a consistency condition at the four corners of an extended lattice is satisfied. Using a boundary condition that only affects the holonomies, we trade this consistency condition for a conditional sampling problem, which reduces to sampling $X,Y\\in\\mathrm{SU}(N)$ given the group commutator $Z=XYX^\\dagger Y^\\dagger$, where $Z\\in\\mathrm{SU}(N)$ depends on the four corners. Plaquettes are sampled independently, and the resulting configurations carry weights due to the additional conditional sampling. We obtain the density of $Z$, which determines these weights, in closed form for $\\mathrm{SU}(2)$ and $\\mathrm{SU}(3)$. A normalizing flow models the single-plaquette distribution for $\\mathrm{SU}(2)$ and $\\mathrm{SU}(3)$; for the group-commutator problem we use a closed-form sampler for $\\mathrm{SU}(2)$ and a trained normalizing flow for $\\mathrm{SU}(3)$. In our tests on $2\\times2$ and $32\\times32$ lattices at two couplings each, per-plaquette acceptance rates exceed $99\\%$ and the effective sample size of the final weights is moderate, typically above one half.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09147",
  "author_total": 1,
  "authors": [
    {
      "name": "Javad Komijani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jhshp31enzpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09147",
  "fulltext_url": null,
  "id": "4jhshp31enzpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09147",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7220941217",
  "pdf_url": "https://arxiv.org/pdf/2610.09147",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jhshp31enzpr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.09147",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09147"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting",
  "title_text": "Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/4jhshp31enzpr",
  "venue": "arXiv",
  "versions": []
}