{
  "abstract": "What effective Lagrangian emerges from the spectrum of a Dirac operator in a topologically non-trivial background? We show that the heat kernel $K(\\tau) = \\mathrm{Tr}\\,e^{-\\tau D^2}$ of a self-consistent chiral soliton generates, through a single proper-time integral, all structural components of the Standard Model Lagrangian: - the chiral kinetic and Skyrme terms via the local Seeley-DeWitt expansion ($R^2 > 0.99$), with a quasi-cancellation mechanism ($\\times 22$ suppression per order); - the rotational dynamics via the Berry connection on the moduli space (99.93% of the moment of inertia); - the gauge coupling via the instanton-skyrmion correspondence ($\\alpha \\approx 0.52$, crossing $\\alpha_s^{\\mathrm{QCD}}$); - the topological Wess-Zumino-Witten term $\\Gamma_{\\mathrm{WZW}} = N_c = 3$ exactly, via the chiral heat kernel; - the gauge group $SU(3) \\times SU(2) \\times U(1)$, the Higgs doublet, and three generations ($N_{\\mathrm{gen}} = 3$), via the spectral truncation of the Peter-Weyl algebra on the moduli space (Emergence Paper IV); - the Higgs mass $M_H \\in [118, 130]$ GeV from the spectral invariants of the finite Dirac operator (Emergence Paper IV). A topological mass gap argument proves $0 < \\varepsilon_{\\mathrm{val}} < M_q$ for any monotone hedgehog with $B = 1$. The same spectral function thus generates both the effective Lagrangian (UV) and the mass gap (IR). The total action takes the form $$S = \\int_{\\mathcal{M}_{B=1}} d\\mu(q) \\int_0^\\infty w(\\hat\\tau)\\, K(\\hat\\tau;\\, q)\\, d\\hat\\tau\\,,$$ a double integral over proper time and moduli space, where $K(\\hat\\tau;\\, q)$ is a universal function determined by topology ($B = 1$) and self-consistency ($F^* = G[F^*]$) alone. Table 2 provides a term-by-term emergence dictionary mapping each component of $\\mathcal{L}_{\\mathrm{SM}}$ to a spectral mechanism; Table 3 maps each Standard Model entity to its solitonic origin.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Fabien Déchery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a0kpwr207ym12.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "a0kpwr207ym12",
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  "landing_url": "https://hal.science/hal-05793301v2",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
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      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-mp"
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      "1.phys.hthe"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05793301/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a0kpwr207ym12.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05793301",
      "source": "hal",
      "url": "https://hal.science/hal-05793301v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.hthe",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.nucl",
      "subfield": "nuclear"
    }
  ],
  "title": "From Spectrum to Action: Emergent Gauge Lagrangian and Topological Mass Gap",
  "title_text": "From Spectrum to Action: Emergent Gauge Lagrangian and Topological Mass Gap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/a0kpwr207ym12",
  "venue": "HAL",
  "versions": []
}