{
  "abstract": "We study the singlet sector of large-$N$, $O(N)$ vector model on $S^1_β\\times S^2_r$ in presence of an angular potential $Ω$. We compute the free energy of the model both at the free fixed point as well as the non-trivial fixed point. The model undergoes a phase transition when the temperature $T$ and angular potential attain the relation $T^2r^2\\sim N (1-ω^2)$, where $ω=rΩ$ and $r$ is the radius of $S^2$, with $Tr\\gg1$, at both the fixed points, with different numerical coefficients. The transition was studied earlier at zero angular potential at $Tr\\sim \\sqrt{N}$. The holonomy eigenvalue distribution, having support on the full circle below the transition, develops a gap above it, called the Gross-Witten-Wadia transition. The angular potential introduces an additional parameter to such a transition, tuning it, the transition can occur even at a fixed temperature. We show that for the free model transition can occur as $1-ω^2\\sim 1/N$ while $Tr\\sim O(1)$. For the interacting model the computation is performed at a limit $Tr\\gg1$, thus we show the same at a large but fixed temperature which does not scale as $\\sqrt{N}$. In the ungapped phase, the free energy exhibits a double pole near $ω^2=1$ for both the fixed points. This is possibly due to the fact that the theory projected onto the singlets is non-local and therefore need not obey the leading simple pole scaling of a local thermal effective action.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09815",
  "author_total": 1,
  "authors": [
    {
      "name": "Srijan Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbg41mkc1wyqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09815",
  "fulltext_url": null,
  "id": "bbg41mkc1wyqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09815",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7221006357",
  "pdf_url": "https://arxiv.org/pdf/2610.09815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbg41mkc1wyqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.09815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09815"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Singlet sector of the vector model with angular potential",
  "title_text": "Singlet sector of the vector model with angular potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/bbg41mkc1wyqb",
  "venue": "arXiv",
  "versions": []
}