{
  "abstract": "Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding $n\\to-n$ while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in $n$. On a fixed marked Euclidean replica filling the same change of variables gives $Z_q[n;\\mathcal J_+]=Z_q[-n;\\mathcal J_+]$, so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle $μ$ conjugate to the entangling-region charge, $Z_q[n;μ]=Z_q[-n;-μ]$, so the symmetry-resolved spectrum obeys $\\mathcal Z_q(\\mathcal Q;n)=\\mathcal Z_q(-\\mathcal Q;-n)$ and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump $(c/3)\\log(1+\\sqrt2)$. Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts $δ\\widehat M=16πGv^2|n|$ and $|δ\\widehat j|=16πGv^2n^2/(mL)$ and, conditionally, a finite continuous winding envelope.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29562",
  "author_total": 1,
  "authors": [
    {
      "name": "Kumar Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70ctd7d23qj80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29562",
  "fulltext_url": null,
  "id": "70ctd7d23qj80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29562",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7214382806",
  "pdf_url": "https://arxiv.org/pdf/2609.29562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70ctd7d23qj80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29562"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Holonomy Separation and Anyonic Hair in AdS$_3$",
  "title_text": "Holonomy Separation and Anyonic Hair in AdS_3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/70ctd7d23qj80",
  "venue": "arXiv",
  "versions": []
}