{
  "abstract": "We set up a truncated numerical approach in the Polyakov bootstrap (PB) framework. We employ a gradient descent optimization to solve PB sum rules numerically, and hence solve crossing for arbitrary deformations of the generalized free field (GFF) spectrum in an iterative way starting from a perturbative solution. For unitary deformations the solutions coincide with extremal CFT spectra. But more interestingly, our findings indicate that a general crossing solution, not necessarily unitary (i.e. without positivity), can be uniquely identified by a smooth connection to GFF. The truncated Polyakov bootstrap approach is established through a number of examples in both single and mixed correlator settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01732",
  "author_total": 3,
  "authors": [
    {
      "name": "Kaushik Kangshabanik"
    },
    {
      "name": "Apratim Kaviraj"
    },
    {
      "name": "Shailesh Lal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32xjdv7tpkrgp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01732",
  "fulltext_url": null,
  "id": "32xjdv7tpkrgp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01732",
  "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": "W7207734989",
  "pdf_url": "https://arxiv.org/pdf/2609.01732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32xjdv7tpkrgp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01732"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Truncated Polyakov bootstrap",
  "title_text": "Truncated Polyakov bootstrap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/32xjdv7tpkrgp",
  "venue": "arXiv",
  "versions": []
}