{
  "id": "2108.12852",
  "version": "v1",
  "published": "2021-08-29T14:26:45.000Z",
  "updated": "2021-08-29T14:26:45.000Z",
  "title": "3-form Yang-Mills based on 2-crossed modules",
  "authors": [
    "Danhua Song",
    "Ke Wu",
    "Jie Yang"
  ],
  "comment": "13 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we study the higher Yang-Mills theory in the framework of higher gauge theory. It was shown that the 2-form electromagnetism can be generalized to the 2-form Yang-Mills theory with the group $U(1)$ replaced by a crossed module of Lie groups. To extend this theory to even higher structure, we develop a 3-form Yang-Mills theory with a 2-crossed module of Lie groups. First, we give an explicit construction of non-degenerate symmetric $G$-invariant forms on the 2-crossed module of Lie algebras. Then, we derive the 3-Bianchi-Identities for 3-curvatures. Finally, we create a 3-form Yang-Mills action and obtain the corresponding field equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-29T14:26:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie groups",
      "higher gauge theory",
      "higher yang-mills theory",
      "higher structure",
      "explicit construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}