{
  "abstract": "We study thermal order in conformal field theories (CFTs) in $d=4-ε$ and $d=3$ dimensions where several scalars are coupled to an $O(N)$ vector field. In $(4-ε)$ dimensions, we consider models coupling a cubic model of $M$ scalars with $\\mathbb{Z}_2^M\\rtimes S_M$ symmetry (corresponding to sign flips and permutations of the scalars) to an $O(N)$ vector model. For any $M$, we find a window of $N$ in which two Wilson-Fisher-like fixed points exist. We show that the $\\mathbb{Z}_2^M\\rtimes S_M$ symmetry is spontaneously broken at arbitrary nonzero temperatures for $M=2$ and sufficiently large $N$ within this window, but it remains unbroken for $M>2$. Using the functional renormalisation group to continue these fixed points towards three dimensions, we find that they collide and move into the complex plane well before reaching $d=3$, suggesting that their continuation to $d=3$ does not yield unitary CFTs. We then work directly in three dimensions at large but finite $N$, with $M\\ll N$, initially without assuming any permutation symmetry among the $M$ scalars. By studying the RG flow, we show that these models possess a conformal manifold up to the leading nontrivial order in the $1/N$ expansion of the beta functions (which is $\\mathcal{O}(1/N)$). At each point on this manifold, the scalars split into two classes that are distinguished by how they couple to the $O(N)$ vector field. We then restrict to a subspace of the conformal manifold where there is an additional symmetry under permutations of the scalars within each class. We prove that in a domain of this subspace, all $M$ scalars acquire thermal expectation values such that the symmetry under sign flips of the scalars is spontaneously broken at all nonzero temperatures. This provides a novel class of large $N$ CFTs that exhibit a rich pattern of persistent symmetry breaking at nonzero temperatures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00160",
  "author_total": 4,
  "authors": [
    {
      "name": "Soumyadeep Chaudhuri"
    },
    {
      "name": "Bilal Hawashin"
    },
    {
      "name": "Eliezer Rabinovici"
    },
    {
      "name": "Michael M. Scherer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ngfh03qd0w7b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00160",
  "fulltext_url": null,
  "id": "0ngfh03qd0w7b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00160",
  "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.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7206166969",
  "pdf_url": "https://arxiv.org/pdf/2609.00160",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ngfh03qd0w7b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.00160",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00160"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Exploring thermal order in conformal theories with multiple scalars coupled to an $O(N)$ vector field",
  "title_text": "Exploring thermal order in conformal theories with multiple scalars coupled to an O(N) vector field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/0ngfh03qd0w7b",
  "venue": "arXiv",
  "versions": []
}