{
  "abstract": "We investigate the trans-series structure of the cusp anomalous dimension of $\\mathcal{N}=4$ supersymmetric Yang-Mills theory and the dynamically generated mass gap of the $\\mathrm{O}(6)$ sigma model at strong 't Hooft coupling. We consider the one-parameter deformation of the cusp anomalous dimension, known as the tilted cusp, and review its strong-coupling expansion obtained through its representation in terms of Fredholm determinants with a matrix Bessel kernel. The advantage of this deformation is that the non-perturbative scales separate naturally, revealing structures that remain hidden in the physical limit. Motivated by this observation, we introduce the tilted mass gap, which reduces to the physical $\\mathrm{O}(6)$ mass gap at a special value of the deformation parameter and exhibits a deep connection with the tilted cusp. This formulation allows us to determine the complete strong-coupling trans-series and resurgence structure of the $\\mathrm{O}(6)$ mass gap, while extending and proving conjectured relations between successive non-perturbative corrections. Building on the underlying Fredholm determinant representation, we construct an Alien calculus that generates all non-perturbative sectors of these AdS/CFT observables directly from their perturbative expansions. Finally, we derive an exact all-orders relation between the strong-coupling trans-series of the $\\mathrm{O}(6)$ mass gap and the cusp anomalous dimension of planar $\\mathcal{N}=4$ supersymmetric Yang-Mills theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.13140",
  "author_total": 2,
  "authors": [
    {
      "name": "Bercel Boldis"
    },
    {
      "name": "Dennis le Plat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ay4nvxm0zvqn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.13140",
  "fulltext_url": null,
  "id": "ay4nvxm0zvqn0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.13140",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7168636732",
  "pdf_url": "https://arxiv.org/pdf/2607.13140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ay4nvxm0zvqn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2607.13140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.13140"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework",
  "title_text": "From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/ay4nvxm0zvqn0",
  "venue": "arXiv",
  "versions": []
}