{
  "abstract": "We determine the maximal torus topological entanglement entropy (TEE) at bounded torus ground-state degeneracy within simply connected untwisted Wess--Zumino--Witten theories. For a fixed modular tensor category $\\mathcal C$, maximization over normalized torus ground states gives $\\max_ψΓ_{T^2}(ψ)=2\\log{\\mathcal D(\\mathcal C)}$, attained in particular by the vacuum-flux state. The remaining problem is therefore to maximize total $\\mathcal D$ at bounded categorical rank. For a simple WZW category $\\mathcal C(\\mathfrak g,k)$, write $r(\\mathfrak g,k)$ and $\\mathcal D(\\mathfrak g,k)$ for its categorical rank and total quantum dimension, and define $F_{\\WZW}(R)=\\sup_{r(\\mathfrak g,k)\\leq R}2\\log\\mathcal D(\\mathfrak g,k)$. We prove the sharp asymptotic law $\\lim_{R\\to\\infty}\\frac{F_{\\WZW}(R)}{(\\log_2R)^2} =\\frac{7ζ(3)}{4π^2}.$ The balanced symplectic sequence $Sp(2n)_n$ attains the coefficient. The constant arises from the odd Fourier modes of the type-$C$ root product at equal rank and level. A sharp entropy--spectral inequality, rank-level duality, and fixed-rank estimates give the global upper bound. A separate corollary extends the same leading law to semisimple WZW categories,equivalently finite Deligne products of simple factors. The unrestricted TQFT envelope remains open; the theorem is sharp within the stated WZW class and supplies a constructive lower bound for the general problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20333",
  "author_total": 1,
  "authors": [
    {
      "name": "Ce Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4rys5m3hxfrvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20333",
  "fulltext_url": null,
  "id": "4rys5m3hxfrvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20333",
  "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",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7203921579",
  "pdf_url": "https://arxiv.org/pdf/2608.20333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4rys5m3hxfrvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2608.20333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20333"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Maximal Total Quantum Dimension at Bounded Rank in WZW Modular Tensor Categories",
  "title_text": "Maximal Total Quantum Dimension at Bounded Rank in WZW Modular Tensor Categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/4rys5m3hxfrvh",
  "venue": "arXiv",
  "versions": []
}