{
  "abstract": "We evaluate exactly the radial metric factor $h(ζ)$ generated by Schwarzian averaging in the AdS$_2$ throat of an extremal Reissner--Nordström AdS$_5$ black brane. The result is a Gaussian integral against $\\coth(πy)$, valid at all radial depths, which Mordell's identity turns into an exact Appell--Lerch $q/q^\\ast$-series representation. The dual series identifies the nonperturbative scale $e^{-π^2 C/ζ}$ missed by any finite near-boundary truncation. The third parametric derivative required by the evaluation generates the quasimodular Eisenstein series $E_2$, absent from the classical Mordell identity. From the integral representation we prove that $\\mathcal{G}_0(ζ):=h(ζ)/ζ^2$ is completely monotone and hence has no interior minimum, so any confining minimum produced by a finite near-boundary truncation is an artifact. We also compute the exact relative variance of the Schwarzian kernel, which makes the averaged-metric approximation error quantitative and shows that the absence of a confining minimum is robust across moment-based effective geometries. Applied to the temporal rectangular Wilson loop, the exact throat gives algebraic screening, $E(L)\\sim -κ_{\\rm IR}/L^2$, the Wilson-loop diagnostic of the semi-local quantum-liquid IR of the extremal RN brane. A numerical check in a simple matched geometry confirms that the screened saddle is the dominant string configuration, and an exact-versus-truncated force comparison shows that the apparent constant-force regime of the fourth-order truncation is not a feature of the exact geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. High Energ. Phys. 2026, 215 (2026)",
  "arxiv": "2607.03120",
  "author_total": 1,
  "authors": [
    {
      "name": "Miguel Tierz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/740t0xa20yejx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03120",
  "fulltext_url": null,
  "id": "740t0xa20yejx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03120",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.03120",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/740t0xa20yejx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2607.03120",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03120"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Exact Schwarzian Metric Factor and Holographic Wilson-Loop Screening",
  "title_text": "Exact Schwarzian Metric Factor and Holographic Wilson-Loop Screening",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/740t0xa20yejx",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/jhep09(2026)215",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}