{
  "id": "2306.02485",
  "version": "v1",
  "published": "2023-06-04T21:31:34.000Z",
  "updated": "2023-06-04T21:31:34.000Z",
  "title": "Study of gapped phases of 4d gauge theories using temporal gauging of the $\\mathbb{Z}_N$ 1-form symmetry",
  "authors": [
    "Mendel Nguyen",
    "Yuya Tanizaki",
    "Mithat Ünsal"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "hep-th",
    "cond-mat.str-el"
  ],
  "abstract": "To study gapped phases of $4$d gauge theories, we introduce the temporal gauging of $\\mathbb{Z}_N$ $1$-form symmetry in $4$d quantum field theories (QFTs), thereby defining effective $3$d QFTs with $\\widetilde{\\mathbb{Z}}_N\\times \\mathbb{Z}_N$ $1$-form symmetry. In this way, spatial fundamental Wilson and 't Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the $4$d QFT, the $\\widetilde{\\mathbb{Z}}_N\\times \\mathbb{Z}_N$ symmetry must be spontaneously broken to an order-$N$ subgroup $H$, and we can classify the $4$d gapped phases by specifying $H$. This establishes the $1$-to-$1$ correspondence between the two classification schemes for gapped phases of $4$d gauge theories: One is the conventional Wilson-'t Hooft classification, and the other is the modern classification using the spontaneous breaking of $4$d $1$-form symmetry enriched with symmetry-protected topological states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-04T21:31:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gapped phases",
      "4d gauge theories",
      "temporal gauging",
      "form symmetry",
      "conventional wilson-t hooft classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}