{
  "id": "1912.02817",
  "version": "v1",
  "published": "2019-12-05T18:59:58.000Z",
  "updated": "2019-12-05T18:59:58.000Z",
  "title": "Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases",
  "authors": [
    "Ryan Thorngren",
    "Yifan Wang"
  ],
  "comment": "53 pages, 7 figures",
  "categories": [
    "hep-th",
    "cond-mat.str-el",
    "math.QA"
  ],
  "abstract": "We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe 't Hooft anomalies and classify gapped phases stabilized by these symmetries, including new 1+1D topological phases. The algebra of these operators is not a group but rather is described by their fusion ring and crossing relations, captured algebraically as a fusion category. Such data defines a Turaev-Viro/Levin-Wen model in 2+1D, while a 1+1D system with this fusion category acting as a global symmetry defines a boundary condition. This is akin to gauging a discrete global symmetry at the boundary of Dijkgraaf-Witten theory. We describe how to \"ungauge\" the fusion category symmetry in these boundary conditions and separate the symmetry-preserving phases from the symmetry-breaking ones. For Tambara-Yamagami categories and their generalizations, which are associated with Kramers-Wannier-like self-dualities under orbifolding, we develop gauge theoretic techniques which simplify the analysis. We include some examples of CFTs with fusion category symmetry derived from Kramers-Wannier-like dualities as an appetizer for the Part II companion paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-05T18:59:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fusion category symmetry",
      "gapped phases",
      "anomaly in-flow",
      "boundary condition",
      "gauge theoretic techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}