{
  "abstract": "We study the Yang-Mills gradient flow of center vortices in SU(2) gauge theory. For axially symmetric vortices the flow reduces exactly to a linear diffusion equation for the radial profile: a Gaussian core keeps its shape while its width grows as $\\sqrt{R^2+4t}$, the flux is exactly conserved, and the thin vortex is the unique bounded fixed point, though not an attractor. Off-diagonal perturbations are governed by a pair of radial Schrödinger operators, and a variational computation shows that, frozen at any instant, the Abelian core has a tachyonic mode for every winding $n\\geq 1$. Since the core spreads while the mode grows, we pass to self-similar variables, where the unstable modes are known in closed form, with growth exponents $μ_{n,m}=n-1+m$. Multiply wound vortices are therefore unstable, while the fundamental vortex is exactly marginal and stays Abelian. A scaling argument rules out any static vortex in the transverse plane, and the instability acquires a simple geometric meaning that shortens the path traced in SU(2) by the holonomy of a growing loop, lowering the winding by two. The flow thus drives every vortex toward the Abelian core of winding $n \\bmod 2$, with non-Abelian structure appearing only as the transient through which multiply wound cores unwind.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33874",
  "author_total": 1,
  "authors": [
    {
      "name": "A. M. Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ez7evg3st2126.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33874",
  "fulltext_url": null,
  "id": "ez7evg3st2126",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33874",
  "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",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7223842609",
  "pdf_url": "https://arxiv.org/pdf/2610.33874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ez7evg3st2126.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Fixed Points of the Yang-Mills Gradient Flow in the Vortex Sector",
  "title_text": "Fixed Points of the Yang-Mills Gradient Flow in the Vortex Sector",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ez7evg3st2126",
  "venue": "arXiv",
  "versions": []
}