{
  "abstract": "We study planar $\\mathcal{N}=4$ super Yang-Mills theory (SYM) on the real projective space $\\mathbb{RP}^4$ using integrability, holography and supersymmetric localization, and discuss its relation to orientifolds in string theory. We show that the integrability of $\\mathcal{N}=4$ SYM is preserved when combining the $\\mathbb{Z}_2$ involution defining $\\mathbb{RP}^4$ with the action of the charge conjugation of the SU$(N)$ gauge group. We demonstrate this by calculating one-point functions of non-BPS single-trace operators in various subsectors at weak coupling, which can be mapped to overlaps between energy eigenstates and crosscap states in integrable spin chains. The results exhibit a parity selection rule, a hallmark of integrability, and are given in terms of a ratio of determinants. Building on these results, we conjecture a closed formula for general single-trace operators. We further provide evidence that this construction is holographically dual to a probe orientifold O1-plane in $\\text{AdS}_5\\times \\text{S}^5$ by constructing the corresponding worldsheet crosscap states in the pp-wave limit. Finally, we use supersymmetric localization to compute one-point functions of half-BPS operators exactly at finite $g_{\\rm YM}$ and $N$. The computation reduces to two-dimensional Yang-Mills theory on $\\mathbb{RP}^2$ twisted by charge conjugation and leads to a matrix integral of a Wishart-Laguerre type. In the planar limit, the exact result interpolates between the weak-coupling gauge-theory result, the strong-coupling supergravity prediction for the orientifold, and the worldsheet crosscap in the pp-wave limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28725",
  "author_total": 4,
  "authors": [
    {
      "name": "Joao Caetano"
    },
    {
      "name": "Shota Komatsu"
    },
    {
      "name": "Paolo Soresina"
    },
    {
      "name": "Anders Wallberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79pfp6m6kftkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28725",
  "fulltext_url": null,
  "id": "79pfp6m6kftkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28725",
  "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",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223229707",
  "pdf_url": "https://arxiv.org/pdf/2610.28725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79pfp6m6kftkb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.28725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28725"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Orientifold and Integrability: $\\mathcal{N}=4$ Super-Yang-Mills on $\\mathbb{RP}^4$",
  "title_text": "Orientifold and Integrability: 𝒩=4 Super-Yang-Mills on ℝℙ^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/79pfp6m6kftkb",
  "venue": "arXiv",
  "versions": []
}