{
  "id": "1912.13069",
  "version": "v1",
  "published": "2019-12-30T19:46:39.000Z",
  "updated": "2019-12-30T19:46:39.000Z",
  "title": "Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry",
  "authors": [
    "Clay Cordova",
    "Kantaro Ohmori"
  ],
  "comment": "4 pages, 1 figure",
  "categories": [
    "hep-th",
    "cond-mat.str-el",
    "math-ph",
    "math.AT",
    "math.MP"
  ],
  "abstract": "We prove that in $(3+1)d$ quantum field theories with $\\mathbb{Z}_N$ symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are frequently present in gauge theories as we illustrate in examples. Our results also constrain the long-distance behavior of certain condensed matter systems such as Weyl-semimetals and may have applications to crystallographic phases with symmetry protected topological order. These results may be viewed as analogs of the Lieb-Schultz-Mattis theorem for continuum field theories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T19:46:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete chiral symmetry",
      "gapped phases",
      "anomaly constraints",
      "quantum field theories",
      "continuum field theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}