{
  "abstract": "We study the one-loop renormalization group flow of the translation-invariant noncommutative pseudoscalar Yukawa theory on four-dimensional Euclidean Moyal space. The two inequivalent orderings of the Moyal-star Yukawa vertex give rise to two independent couplings $g_{1}$ and $g_{2}$, whose beta functions form a coupled nonlinear system; every one-loop divergence is absorbed by a counterterm already present in the action, establishing one-loop renormalizability of the theory. We solve the one-loop system analytically: it decouples in the variables $u=g_{1}^{2}+g_{2}^{2}$ and $v=g_{1}^{2}-g_{2}^{2}$, the quartic coupling is obtained by a Riccati reduction on the symmetric surface $g_{1}=g_{2}$, and the generic asymmetric flow is reduced to a single quadrature by the exact invariant $\\mathcal{I}=(g_{1}g_{2})^{3}/(g_{1}^{2}-g_{2}^{2})^{4}$. Two dynamical consequences follow. The ratio $r=v/u$ has a UV-attractive symmetric surface $r=0$ and IR-attractive asymmetric directions $r=\\pm1$, so that the flow restores the symmetry between the two Moyal orderings towards the ultraviolet and amplifies any initial ordering asymmetry towards the infrared, as a fractional power of the logarithm. In consequence the Yukawa-induced coefficient of the non-planar $1/(θ^{2}p^{2})$ structure is dynamically suppressed towards $p\\rightarrow 0$; the singularity itself is not removed, and remains the task of the IR-improving term. We also solve the dimensionful sector ($M^{2}$, $m$, $a^{2}$ and $b$) in closed form on the symmetric critical trajectory, and compare throughout with the commutative theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29213",
  "author_total": 2,
  "authors": [
    {
      "name": "Karim Bouchachia"
    },
    {
      "name": "Smain Kouadik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5g4r5kqpjdkpy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29213",
  "fulltext_url": null,
  "id": "5g4r5kqpjdkpy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29213",
  "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-th"
    ],
    [
      "openalex",
      "3109|Noncommutative and Quantum Gravity Theories"
    ]
  ],
  "openalex": "W7204895380",
  "pdf_url": "https://arxiv.org/pdf/2608.29213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5g4r5kqpjdkpy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2608.29213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29213"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "One-loop renormalization group flow of the translation-invariant noncommutative Yukawa theory",
  "title_text": "One-loop renormalization group flow of the translation-invariant noncommutative Yukawa theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/5g4r5kqpjdkpy",
  "venue": "arXiv",
  "versions": []
}