{
  "id": "2007.10354",
  "version": "v1",
  "published": "2020-07-20T18:00:03.000Z",
  "updated": "2020-07-20T18:00:03.000Z",
  "title": "On matrix models and their $q$-deformations",
  "authors": [
    "Luca Cassia",
    "Rebecca Lodin",
    "Maxim Zabzine"
  ],
  "comment": "45 pages, 2 figures",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $\\beta$-deformed Hermitean matrix model and the $q$-deformed matrix models associated to 3d $\\mathcal{N}=2$ supersymmetric gauge theories on $D^2\\times_{q}S^1$ and $S_b^3$ by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the $W$-algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T18:00:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformations",
      "supersymmetric gauge theories",
      "deformed hermitean matrix model",
      "novel results",
      "deformed matrix models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}