{
  "id": "oai:papers.qnfo.org:can-finite-group-topological-quantum-field-theories-generate-continuous-standard",
  "slug": "can-finite-group-topological-quantum-field-theories-generate-continuous-standard",
  "title": "Can Finite‑Group Topological Quantum Field Theories Generate Continuous Standard‑Model Gauge Symmetry?",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The Standard Model (SM) requires a continuous gauge group SU(3)× SU(2)× U(1) with infinitely many charge sectors, while finite‑group Walker‑Wang constructions provide only finitely many superselection sectors. Existing proposals therefore face a gap: no demonstration that a finite‑group braided fusion category can yield the SM gauge symmetry after coarse‑graining. We combine (i) the classification of finite‑group 2‑gauge theories [2], (ii) the excess‑zero property of finite Coxeter groups [1], (iii) the density‑of‑states formula for finite‑group symmetry [3], and (iv) the factorisation of gauge symmetry on intervals [4] to prove a no‑go theorem. The theorem shows that any lattice TQFT whose underlying braided fusion category has a finite simple‑object set can realise at most a finite gauge group whose charge spectrum is bounded by the order |G| of the underlying finite group. Assuming the standard result that Z(Rep(G)) contains exactly |G| simple objects, we obtain a concrete bound for the candidate group G=SL(2,3): |G|=24 and Z(Rep(SL(2,3))) has only five simple objects. Since 5≪∞, the model cannot approximate the continuous SM symmetry. Anomaly‑matching analysis further shows that no assignment of five finite‑group charges can satisfy the SM cubic and mixed gauge‑gravitational anomalies. The result redirects topological‑genesis efforts toward either infinite‑category constructions or alternative emergence mechanisms.",
  "abstract_markdown": "The Standard Model (SM) requires a continuous gauge group $SU(3)\\times SU(2)\\times U(1)$ with infinitely many charge sectors, while finite‑group Walker‑Wang constructions provide only finitely many superselection sectors.  Existing proposals therefore face a gap: no demonstration that a finite‑group braided fusion category can yield the SM gauge symmetry after coarse‑graining.  We combine (i) the classification of finite‑group 2‑gauge theories [2], (ii) the excess‑zero property of finite Coxeter groups [1], (iii) the density‑of‑states formula for finite‑group symmetry [3], and (iv) the factorisation of gauge symmetry on intervals [4] to prove a no‑go theorem.  The theorem shows that any lattice TQFT whose underlying braided fusion category has a finite simple‑object set can realise at most a finite gauge group whose charge spectrum is bounded by the order $|G|$ of the underlying finite group.  Assuming the standard result that $Z(\\mathrm{Rep}(G))$ contains exactly $|G|$ simple objects, we obtain a concrete bound for the candidate group $G=SL(2,3)$: $|G|=24$ and $Z(\\mathrm{Rep}(SL(2,3)))$ has only five simple objects.  Since $5\\ll\\infty$, the model cannot approximate the continuous SM symmetry.  Anomaly‑matching analysis further shows that no assignment of five finite‑group charges can satisfy the SM cubic and mixed gauge‑gravitational anomalies.  The result redirects topological‑genesis efforts toward either infinite‑category constructions or alternative emergence mechanisms.",
  "date": "2026-10-25",
  "first_published": "2026-10-25",
  "last_revised": "2026-10-25T00:00:00Z",
  "modified": "2026-10-25T00:00:00Z",
  "version": "1.0.0",
  "version_count": 1,
  "language": "en",
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  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/can-finite-group-topological-quantum-field-theories-generate-continuous-standard",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
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    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/can-finite-group-topological-quantum-field-theories-generate-continuous-standard",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
        "nameType": "Personal",
        "nameIdentifiers": [
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    ],
    "titles": [
      {
        "title": "Can Finite‑Group Topological Quantum Field Theories Generate Continuous Standard‑Model Gauge Symmetry?"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
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    "dates": [
      {
        "date": "2026-10-25",
        "dateType": "Issued"
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        "date": "2026-10-25",
        "dateType": "Updated"
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    "language": "en",
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    "descriptions": [
      {
        "description": "The Standard Model (SM) requires a continuous gauge group SU(3)× SU(2)× U(1) with infinitely many charge sectors, while finite‑group Walker‑Wang constructions provide only finitely many superselection sectors. Existing proposals therefore face a gap: no demonstration that a finite‑group braided fusion category can yield the SM gauge symmetry after coarse‑graining. We combine (i) the classification of finite‑group 2‑gauge theories [2], (ii) the excess‑zero property of finite Coxeter groups [1], (iii) the density‑of‑states formula for finite‑group symmetry [3], and (iv) the factorisation of gauge symmetry on intervals [4] to prove a no‑go theorem. The theorem shows that any lattice TQFT whose underlying braided fusion category has a finite simple‑object set can realise at most a finite gauge group whose charge spectrum is bounded by the order |G| of the underlying finite group. Assuming the standard result that Z(Rep(G)) contains exactly |G| simple objects, we obtain a concrete bound for the candidate group G=SL(2,3): |G|=24 and Z(Rep(SL(2,3))) has only five simple objects. Since 5≪∞, the model cannot approximate the continuous SM symmetry. Anomaly‑matching analysis further shows that no assignment of five finite‑group charges can satisfy the SM cubic and mixed gauge‑gravitational anomalies. The result redirects topological‑genesis efforts toward either infinite‑category constructions or alternative emergence mechanisms.",
        "descriptionType": "Abstract"
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}