{
  "abstract": "False vacuum decay in scalar field theory is thought to be dominated by Coleman's O(4)-symmetric bounce, the minimum action nontrivial solution of the imaginary-time equations of motion. Beyond the bounce, non-constructive existence proofs of O(4)-breaking solutions are available in the mathematics literature, but the solutions themselves, and their physics, have remained unknown. Considering the simple, bounded-below, scalar field potential $V(ϕ)=\\frac{m^2}{2}ϕ^2-\\fracλ{4}ϕ^4+\\frac{g}{6}ϕ^6$, we construct a nonradial solution explicitly: two bubble tubes of opposite sign wrapping orthogonal rings, invariant under ${\\rm O}(2)\\times{\\rm O}(2)$ rotations combined with a $Z_2$ symmetry that exchanges the rings. The solution admits valid Cauchy data for real-time evolution from a $t=0$ slice, and supports an odd $>1$ number of unstable deformation modes. Having found this first solution we proceed to discover additional examples, in 3d as well as other 4d theories including a $Z_2$-violating potential and scalar QED for which there were no previously known existence proofs or O(4)-dominance theorems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16024",
  "author_total": 4,
  "authors": [
    {
      "name": "Guy Avraham"
    },
    {
      "name": "Kfir Blum"
    },
    {
      "name": "Omri Rosner"
    },
    {
      "name": "Isaac G. Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/553fsd973d4hf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16024",
  "fulltext_url": null,
  "id": "553fsd973d4hf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16024",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.16024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/553fsd973d4hf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2606.16024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16024"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "The O(4)-breaking bubble",
  "title_text": "The O(4)-breaking bubble",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/553fsd973d4hf",
  "venue": "arXiv",
  "versions": []
}