{
  "id": "1907.00493",
  "version": "v1",
  "published": "2019-06-30T22:55:14.000Z",
  "updated": "2019-06-30T22:55:14.000Z",
  "title": "Nested coordinate Bethe wavefunctions from the Bethe/gauge correspondence",
  "authors": [
    "Omar Foda",
    "Masahide Manabe"
  ],
  "comment": "33 pages, 13 figures",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In [1, 2], Nekrasov applied the Bethe/gauge correspondence to derive the $\\mathfrak{su}\\, (2)$ XXX spin-chain coordinate Bethe wavefunction from the IR limit of a 2D $\\mathcal{N}=(2, 2)$ supersymmetric $A_1$ quiver gauge theory with an orbifold-type codimension-2 defect. Later, Bullimore, Kim and Lukowski implemented Nekrasov's construction at the level of the UV $A_1$ quiver gauge theory, recovered his result, and obtained further extensions of the Bethe/gauge correspondence [3]. In this work, we extend the construction of the defect to $A_M$ quiver gauge theories to obtain the $\\mathfrak{su} \\, ( M + 1 )$ XXX spin-chain nested coordinate Bethe wavefunctions. The extension to XXZ spin-chain is straightforward. Further, we apply a Higgsing procedure to obtain more general $A_M$ quivers and the corresponding wavefunctions, and interpret this procedure (and the Hanany-Witten moves that it involves) on the spin-chain side in terms of Izergin-Korepin-type specializations (and re-assignments) of the parameters of the coordinate Bethe wavefunctions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-30T22:55:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bethe/gauge correspondence",
      "quiver gauge theory",
      "xxx spin-chain coordinate bethe wavefunction",
      "spin-chain nested coordinate bethe wavefunctions",
      "xxx spin-chain nested coordinate bethe"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}