{
  "abstract": "We investigate complex Langevin (CL) dynamics for real-time SU($N$) gauge theories in 3+1 dimensions and introduce new kernel modifications tailored for lattice gauge theory (LGT). Using the anisotropic kernel as a baseline, we demonstrate that on a rectangular regularized Schwinger-Keldysh time contour, stable simulations are possible for pure SU(2) gauge theory up to a real-time extent of $2β$ at a bare coupling $g=0.5$, where $β$ denotes the inverse temperature. We show that a contour-dependent phase kernel extends this reach to $3β$, while a local, field-dependent kernel based on traced plaquettes achieves $3.5β$. These constructions represent the first application of such kernels to LGTs, especially in 3+1 dimensions. To validate the approach, we generalize the CL correctness criterion based on the drift magnitude to kernelled dynamics, providing a practical tool to assess correct convergence. Our results substantially advance the applicability of CL to real-time simulations in Minkowski space, establishing a framework for controlled studies of non-Abelian gauge theories at unprecedented time scales. A forthcoming paper applies these developments to the computation of unequal-time correlation functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37800",
  "author_total": 3,
  "authors": [
    {
      "name": "Kirill Boguslavski"
    },
    {
      "name": "Paul Hotzy"
    },
    {
      "name": "David I. Müller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57cggxgmm2wvj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37800",
  "fulltext_url": null,
  "id": "57cggxgmm2wvj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37800",
  "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-lat"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37800",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57cggxgmm2wvj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.37800",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37800"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Complex Langevin kernels for real-time SU(N) lattice gauge theory in 3+1 dimensions",
  "title_text": "Complex Langevin kernels for real-time SU(N) lattice gauge theory in 3+1 dimensions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/57cggxgmm2wvj",
  "venue": "arXiv",
  "versions": []
}