{
  "annotation_id": "9616927b-c160-42d2-b761-0543ed9e3a19",
  "date_created": "2026-02-17T05:53:12.484000Z",
  "date_modified": "2026-02-17T05:53:12.484000Z",
  "file_hash": "90f05d0e431504a2a93b195e6212ac47b1114d197216f88392d8c913cd29729e",
  "private": false,
  "record": {
    "abstract": "We study an Aganagic-Vafa brane supported on a special Lagrangian submanifold $\\mathcal{L}$ in a non-compact toric Calabi-Yau threefold $\\mathcal{X}$. From the perspective of geometric engineering, the Aganagic-Vafa branes give rise to a special class of half-BPS codimension-two defects in 5d $\\mathcal{N}=1$ supersymmetric field theories in the presence of $\\Omega$-background. We propose that the defect partition functions give generating functions of refined, non-negative, integral open BPS invariants of the pair $(\\mathcal{X},\\mathcal{L})$, across different K\\\"{a}hler moduli chambers they are expanded in. In the Nekrasov-Shatashvili limit, the partition function provides a partially resummed solution to a $q$-difference equation that quantizes the mirror curve of $\\mathcal{X}$ in an unambiguous fashion, in a polarization determined by the discrete labels of the Aganagic-Vafa brane. We demonstrate our method at examples of $\\mathbb{C}^3$, resolved conifold, resolved $A_1$-singularity, local $F_0$, and local $F_1$.",
    "arxiv_id": "2601.07662",
    "authors": [
      "Sibasish Banerjee",
      "Nafiz Ishtiaque",
      "Saebyeok Jeong"
    ],
    "categories": [
      "hep-th",
      "math-ph",
      "math.AG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Refined Invariants and Quantum Curves from Supersymmetric Localization",
    "url": "https://arxiv.org/abs/2601.07662",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6389ce8b-a257-434b-ba3b-c01c66d259bd",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}