{
  "abstract": "We construct 2d $\\mathcal{N}=(2,2)$ gauged linear sigma models with $\\mathrm{U}(1|1)^N$ supergauge group possibly with superpotential. Despite being nonunitary, one can still study their space of supersymmetric states and explore their applications to mathematics. In particular, we find a relation between a nonlinear sigma model on a Calabi-Yau complete intersection of hypersurfaces in a super-Grassmannian and a supergauged Landau-Ginzburg orbifold, which can reduce to a regular Calabi-Yau/Landau-Ginzburg correspondence for complete intersections. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Clader [1] and Zhao [2]. Similarly, we find a relation between a nonlinear sigma model on a Calabi-Yau hypersurface in a product of super-Grassmannians and a hybrid NLSM/supergauged Landau-Ginzburg orbifold, which can reduce to a regular hybrid Calabi-Yau/Landau-Ginzburg correspondence for hypersurfaces in product space. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Fan-Jarvis-Ruan [3]. We also find that Calabi-Yau supervector bundles over a super-Grassmannian can undergo a physically related mild topology change which is reducible to a regular Atiyah-type flop transition. This defines a super-Grassmannian generalization of a birational equivalence of Calabi-Yau vector bundles in mathematics. Similarly, we find that a Calabi-Yau complete intersection of quadrics in a super-Grassmannian can also undergo a physically related topology change which is reducible to a regular conifold transition. This defines a super-Grassmannian generalization of a homological projective duality for Calabi-Yau quadrics by Kuznetsov-Perry [4] in mathematics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19775",
  "author_total": 3,
  "authors": [
    {
      "name": "Arif Er"
    },
    {
      "name": "Zhangcheng Liu"
    },
    {
      "name": "Meng-Chwan Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95wqaqsgdky8c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19775",
  "fulltext_url": null,
  "id": "95wqaqsgdky8c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19775",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7203925599",
  "pdf_url": "https://arxiv.org/pdf/2608.19775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95wqaqsgdky8c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2608.19775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Supergroup Gauged Linear Sigma Models and their Physical Mathematics",
  "title_text": "Supergroup Gauged Linear Sigma Models and their Physical Mathematics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/95wqaqsgdky8c",
  "venue": "arXiv",
  "versions": []
}