{
  "id": "2502.07573",
  "version": "v1",
  "published": "2025-02-11T14:16:15.000Z",
  "updated": "2025-02-11T14:16:15.000Z",
  "title": "Gauge Origami and BPS/CFT correspondence",
  "authors": [
    "Go Noshita"
  ],
  "comment": "PhD thesis submitted to Department of Physics, University of Tokyo (Dec. 2024), 174 pages. Based on arXiv:2310.08545 and arXiv:2411.01987",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA",
    "math.RT"
  ],
  "abstract": "Gauge origami is a generalized supersymmetric gauge theory defined on several intersecting space-time components. It provides a systematic way to consider generalizations of instantons. In this thesis, we explore the gauge origami system in $\\mathbb{R}^{1,1}\\times \\mathbb{C}^{4}$ and its BPS/CFT correspondence. String theoretically, instantons of the gauge origami system arise from D0-branes bound to D$(2p)$-branes wrapping cycles in $\\mathbb{C}^{4}$. The low energy theory of the D0-branes is understood as an $\\mathcal{N}=2$ supersymmetric quiver quantum mechanical system and the Witten index of it produces the instanton partition function. We define a $q$-deformed quiver Cartan matrix associated to this quiver structure and introduce vertex operators associated with the D-branes and show that the contour integral formula for the Witten index has a nice free field realization. Such free field realization leads to the concept of BPS $qq$-characters or BPS quiver W-algebras, which are generalizations of the conventional deformed W-algebras. 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 of the quantum toroidal $\\mathfrak{gl}_{1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-11T14:16:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bps/cft correspondence",
      "gauge origami system",
      "characters",
      "quiver cartan matrix",
      "supersymmetric gauge theory"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 174,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}