{
  "abstract": "We develop a twofold generalization of classical Yang-Mills theory, extending it from principal bundles to the setting of possibly non-transitive and non-integrable Lie algebroids. The classical theory is recovered when one considers the Atiyah algebroid of a principal bundle. In our framework, principal bundle connections are replaced by the more general notion of (infinitesimal) multiplicative Ehresmann connections. An action functional for such connections is constructed, now including a curvature 3-form contribution, alongside the usual curvature 2-form term, and the resulting variational problem is naturally constrained by a cohomological condition. We derive the associated Euler-Lagrange equations, and define a class of self-dual solutions (instantons) in both 4 and 5 dimensions. We also show that the solution space is invariant under gauge transformations, and compute its tangent space at a solution. As an important example, we show that our framework produces a Yang-Mills theory for connections on bundle gerbes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10904",
  "author_total": 1,
  "authors": [
    {
      "name": "Žan Grad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/730emw0xgvpnp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10904",
  "fulltext_url": null,
  "id": "730emw0xgvpnp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10904",
  "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"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7168238399",
  "pdf_url": "https://arxiv.org/pdf/2607.10904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/730emw0xgvpnp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2607.10904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Yang-Mills theory for multiplicative Ehresmann connections",
  "title_text": "Yang-Mills theory for multiplicative Ehresmann connections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/730emw0xgvpnp",
  "venue": "arXiv",
  "versions": []
}