{
  "abstract": "We discuss the finite-$N$ Hilbert space of bilocal operators that underlies bilocal holography of vector models, beyond the sector built on the Fock vacuum. If the microscopic oscillator Fock space carries a multiplicity-free dual action of a compact color group $G$ and a bilocal algebra, Howe duality implies that projection to the derived subgroup $[G,G]$ selects precisely the characters of the abelianization $G^{\\rm ab}=G/[G,G]$ that occur in the Fock space. Thus $O(N)/SO(N)=\\mathbb Z_2$ gives two sectors, $U(N)/SU(N)=U(1)$ gives integer determinant-charge sectors, while $Sp(N)$ is perfect and gives no additional sector; Bose/Fermi statistics and the number of modes determine which sectors are actually realized. We construct the epsilon and determinant backgrounds that generate these sectors, together with their finite-$N$ constraints and Casimirs, and find that the two bosonic $O(N)$ sectors are not distinguished by any Casimir. Using group-integral projectors, we derive explicit sector-resolved characters for the $O(N)$ and $U(N)$ theories. Around each new background we solve the constraints with auxiliary oscillators, which form a Fermi sea for bosonic matter. In the free vector model on $\\mathbb R\\times S^2$ the new sectors consist of baryonic primaries; we determine their energies, degeneracies and spin content exactly at finite $N$, together with their lowest energy at fixed angular momentum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30572",
  "author_total": 5,
  "authors": [
    {
      "name": "Byoungjoon Ahn"
    },
    {
      "name": "Robert de Mello Koch"
    },
    {
      "name": "Vatsal Garg"
    },
    {
      "name": "Antal Jevicki"
    },
    {
      "name": "Junggi Yoon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecdmx71zcj05s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30572",
  "fulltext_url": null,
  "id": "ecdmx71zcj05s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30572",
  "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": "W7223323298",
  "pdf_url": "https://arxiv.org/pdf/2610.30572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecdmx71zcj05s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30572"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Beyond the Fock Vacuum in Finite-$N$ Bilocal Algebras of Vector Models",
  "title_text": "Beyond the Fock Vacuum in Finite-N Bilocal Algebras of Vector Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/ecdmx71zcj05s",
  "venue": "arXiv",
  "versions": []
}