{
  "id": "2111.05206",
  "version": "v3",
  "published": "2021-11-09T15:32:36.000Z",
  "updated": "2022-03-22T19:09:52.000Z",
  "title": "Crystal bases and three-dimensional $ \\mathcal{N}=4 $ Coulomb branches",
  "authors": [
    "Leonardo Santilli",
    "Miguel Tierz"
  ],
  "comment": "ii+60 pages, many figures. v2: minor improvements. v3: clarifications and references added, published version",
  "journal": "J. High Energ. Phys. 2022, 73 (2022)",
  "doi": "10.1007/JHEP03(2022)073",
  "categories": [
    "hep-th",
    "math-ph",
    "math.AG",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We establish and develop a correspondence between certain crystal bases (Kashiwara crystals) and the Coulomb branch of three-dimensional $ \\mathcal{N} =4 $ gauge theories. The result holds for simply-laced, non-simply laced and affine quivers. Two equivalent derivations are given in the non-simply laced case, either by application of the axiomatic rules or by folding a simply-laced quiver. We also study the effect of turning on real masses and the ensuing simplification of the crystal. We present a multitude of explicit examples of the equivalence. Finally, we put forward a correspondence between infinite crystals and Hilbert spaces of theories with isolated vacua.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-03-22T19:09:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coulomb branch",
      "crystal bases",
      "three-dimensional",
      "correspondence",
      "gauge theories"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "J. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}