{
  "abstract": "Multi-winding Wilson loops (Wilson spools) in 2+1-dimensional gravity can reproduce one-loop partition functions of local free fields in the bulk. Bulk free fields have a second-quantized Fock space, and the AdS/CFT correspondence suggests that the associated multi-particle sectors are dual to multi-trace primaries in the CFT. In this note, we use standard symmetric-function methods to show that the Wilson spool in thermal AdS$_3$ can be recast as a sum over $single$-winding Wilson loops -- one for each multi-trace primary. In a companion paper to appear, we will view Wilson networks and TQFTs as the natural language of non-perturbative bulk quantum gravity. The present note illustrates how this can apply to $local$ bulk fields, and not just defects: a bulk (generalized free) field is to be viewed as a full tower of multi-trace Wilson lines. We further show that the $SL(2)$ descendants of each multi-trace primary, together with the boundary gravitons of the AdS$_3$ background, correctly reproduce the full Virasoro character of each module. In this language, the role of a light insertion on a heavy primary is played by a topological Verlinde line. This allows us to obtain a \"microscopic\" description of one-loop determinants on the smooth BTZ handlebody. A spatially wound probe Wilson line on a torus with a contractible $thermal$ cycle can be traded for a Verlinde line inserted on a dense family of heavy Polyakov loops -- with the roles of the two cycles exchanged, so that the $spatial$ cycle is now contractible. The vacuum row of the modular $S$-kernel acts as the (approximate) density of the heavy primaries. This reinforces the case made in arXiv:2601.18775 that a smooth horizon is a stand-in for an ensemble of quantum states, each produced by a heavy Wilson line that appears as a singular horizon in the semi-classical limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21397",
  "author_total": 2,
  "authors": [
    {
      "name": "Vishal Gayari"
    },
    {
      "name": "Chethan Krishnan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f4tp9wd8x45e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21397",
  "fulltext_url": null,
  "id": "7f4tp9wd8x45e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21397",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7170696190",
  "pdf_url": "https://arxiv.org/pdf/2607.21397",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f4tp9wd8x45e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2607.21397",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21397"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Wilson Towers as Local Bulk Fields",
  "title_text": "Wilson Towers as Local Bulk Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/7f4tp9wd8x45e",
  "venue": "arXiv",
  "versions": []
}