{
  "abstract": "We discuss the continuum two-dimensional conformal field theory, whose target space is a two-torus. In addition to its standard zero-form internal symmetries, the model also has a $-1$-form symmetry associated with its $θ$-parameter, which is also known as a background $B$-field. These symmetries combine into a higher group with anomalies. A spatially winding $B$-field generically breaks the spatial translation symmetry completely, and reduces the continuous target-space (internal) momentum symmetry to a (projectively realized) discrete subgroup. When $B$ varies linearly, a discrete translation subgroup survives, and it combines with the internal symmetry into a non-Abelian group, while the other translations survive as non-invertible symmetries. Even though the model lacks the standard spatial translation symmetry, the non-invertible translation symmetry explains why it is solvable via a Fourier decomposition. We then consider a lattice version of this system, using its modified Villain formulation. Surprisingly, all these subtleties in the symmetries of the continuum model exist on a finite lattice. Finally, we discuss various generalizations of this model, demonstrating that the phenomena we uncovered are more broadly valid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22485",
  "author_total": 4,
  "authors": [
    {
      "name": "Yichul Choi"
    },
    {
      "name": "Nathan Seiberg"
    },
    {
      "name": "Sahand Seifnashri"
    },
    {
      "name": "Wucheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3003k6bxa0m5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22485",
  "fulltext_url": null,
  "id": "e3003k6bxa0m5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22485",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7222934353",
  "pdf_url": "https://arxiv.org/pdf/2610.22485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3003k6bxa0m5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22485"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Topological Aspects of the $c=2$ Model in the Continuum and on the Lattice",
  "title_text": "Topological Aspects of the c=2 Model in the Continuum and on the Lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/e3003k6bxa0m5",
  "venue": "arXiv",
  "versions": []
}