{
  "abstract": "We construct perturbative black-brane solutions carrying neutral scalar hair in the $G_{2}$-invariant truncation of four-dimensional dyonic $\\mathcal{N}=8$ ISO(7) gauged supergravity, an exact consistent truncation of massive type~IIA supergravity on $S^{6}$. Expanding around the $G_{2}$-symmetric AdS$_{4}$-Schwarzschild black brane in powers of a dimensionless scalar-charge parameter $\\eps$, we show that the perturbation hierarchy reduces, order by order, to a nested sequence of inhomogeneous Legendre equations (demonstrated through second order). The first-order scalar satisfies a Pöschl--Teller equation with exact parameter $ν(ν+1)=2/3$, giving $ν=-\\frac{1}{2}+\\frac{\\sqrt{33}}{6}$, and the first-order metric is fixed algebraically by the same function, $A^{(1)}=-\\tfrac{\\sqrt{7}}{2}ϕ^{(1)}$, so the entire $\\mathcal{O}(\\eps)$ sector is one Legendre function. An identity $ν+1=Δ_{+}/3$, with $Δ_{+}=(3+\\sqrt{33})/2\\approx 4.372$ the conformal dimension of the dual scalar operator, relates the Pöschl-Teller parameter to the AdS/CFT dictionary via the nonlinear Fefferman-Graham map $z \\propto z_{\\mathrm{FG}}^{3}$. The $\\mathcal{O}(\\eps^{2})$ back-reaction yields explicit corrections to the renormalized free energy and Bekenstein-Hawking entropy density at fixed temperature, consistent with the first law; equivalently, at fixed entropy or energy density it \\emph{lowers} the Hawking temperature by $δT/T=\\mathcal{O}(\\eps^{2})$. For the leading transport coefficients the shear viscosity saturates $η/s=1/(4π)$, while the Eling-Oz horizon formula gives a nonzero bulk viscosity $ζ/η=\\bigl(\\tfrac{Δ_{+}-3}{2}\\bigr)^{2}\\eps^{2}=\\tfrac{3(7-\\sqrt{33})}{8}\\eps^{2}\\approx0.471\\,\\eps^{2}$. With $c_{s}^{2}=\\tfrac12-\\mathcal O(\\eps^{2})<\\tfrac12$, this indicates a softening of the equation of state.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18959",
  "author_total": 1,
  "authors": [
    {
      "name": "Sangheon Yun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6f643fwh386fb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18959",
  "fulltext_url": null,
  "id": "6f643fwh386fb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18959",
  "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"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7203857930",
  "pdf_url": "https://arxiv.org/pdf/2608.18959",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6f643fwh386fb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2608.18959",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18959"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Perturbative Hairy Black Branes in the $G_{2}$-Invariant Sector of Dyonic ISO(7) Gauged Supergravity",
  "title_text": "Perturbative Hairy Black Branes in the G_2-Invariant Sector of Dyonic ISO(7) Gauged Supergravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/6f643fwh386fb",
  "venue": "arXiv",
  "versions": []
}