{
  "abstract": "We identify a mathematical structure in the gap equations of the large- N Gross–Neveu model at imaginary chemical potential in odd spacetime dimensions. Using this model as the primary example, the central observation is an elementary dimensional ladder: a single centred first difference with respect to $$\\sigma ^2$$ σ 2 relates the thermal part of the gap equation in dimension d to that in dimension $$d-2$$ d - 2 , for every odd d . Iterating this elementary step generates the higher-order finite-difference (discrete Laplacian) relations; for the distinguished sequence $$d=4k+3$$ d = 4 k + 3 , whose kernel exponent is even, the closed stencil hierarchy connects d to $$2d-3$$ 2 d - 3 through 2 k iterates. We show that the gap equations can be written as the sum of two parts: one defined by higher-order finite-difference patterns and a cutoff-dependent part given by a truncated asymptotic expansion of a hypergeometric function. The same discrete finite-difference hierarchy is shown to arise in the thermal sector of large- N bosonic models, indicating that the underlying structure is not restricted to fermionic theories. We further argue that this picture suggests a relation between thermal field theories in these odd d dimensions and exactly solvable one-dimensional quantum problems. We find that the thermal mass at specific imaginary chemical potential values corresponds to points where internal-energy and entropy contributions balance, which is formally analogous to OPE inversion formula techniques where thermal mass values arise from sets of transcendental equations.",
  "abstract_shown": true,
  "affiliations": [
    "Aristotle University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Evangelos G. Filothodoros",
      "orcid": "0000-0002-5898-7288"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84vgk4carxc05.bib",
  "cited_by": 0,
  "doi": "10.1140/epjc/s10052-026-16430-4",
  "fulltext_url": "https://doi.org/10.1140/epjc/s10052-026-16430-4",
  "id": "84vgk4carxc05",
  "issns": [
    "1434-6044",
    "1434-6052"
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  "landing_url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16430-4",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QB460-466"
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    [
      "lcc",
      "QC770-798"
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      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
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  "pdf_url": "https://link.springer.com/content/pdf/10.1140/epjc/s10052-026-16430-4.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/84vgk4carxc05.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "10.1140/epjc/s10052-026-16430-4",
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      "url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16430-4"
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  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Quantum Chromodynamics and Particle Interactions",
      "subfield": "high-energy"
    }
  ],
  "title": "Discrete Laplacian structure and kernel reduction of the gap equation in odd-dimensional large-N vector models at imaginary chemical potential",
  "title_text": "Discrete Laplacian structure and kernel reduction of the gap equation in odd-dimensional large-N vector models at imaginary chemical potential",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:46:19Z",
  "url": "https://research.draconitic.com/paper/84vgk4carxc05",
  "venue": "The European Physical Journal C",
  "versions": []
}