{
  "id": "2310.08545",
  "version": "v1",
  "published": "2023-10-12T17:39:55.000Z",
  "updated": "2023-10-12T17:39:55.000Z",
  "title": "Gauge origami and quiver W-algebras",
  "authors": [
    "Taro Kimura",
    "Go Noshita"
  ],
  "comment": "149+36 pages",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We explore the quantum algebraic formalism of the gauge origami system in $\\mathbb{C}^{4}$, where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas have free field interpretations, leading to the operator formalism of $qq$-characters associated with each D-brane. The $qq$-characters of D2 and D4-branes correspond to screening charges and generators of the affine quiver W-algebra, respectively. On the other hand, the $qq$-characters of D6 and D8-branes represent novel types of $qq$-characters, where monomial terms are characterized by plane partitions and solid partitions. The composition of these $qq$-characters yields the instanton partition functions of the gauge origami system, eventually establishing the BPS/CFT correspondence. Additionally, we demonstrate that the fusion of $qq$-characters of D-branes in lower dimensions results in higher-dimensional D-brane $qq$-characters. We also investigate quadratic relations among these $qq$-characters. Furthermore, we explore the relationship with the representations, $q$-characters, and the Bethe ansatz equations of the quantum toroidal $\\mathfrak{gl}_{1}$. This connection provides insights into the Bethe/Gauge correspondence of the gauge origami system from both gauge-theoretic and quantum-algebraic perspectives. We finally present conjectures regarding generalizations to general toric Calabi-Yau four-folds. These generalizations imply the existence of an extensive class of $qq$-characters, which we call BPS $qq$-characters. These BPS $qq$-characters offer a new systematic approach to derive a broader range of BPS/CFT correspondence and Bethe/Gauge correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-12T17:39:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characters",
      "gauge origami system",
      "general toric calabi-yau four-folds",
      "bethe/gauge correspondence",
      "bps/cft correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}