{
  "abstract": "We introduce a formalism for conformal field theory in four dimensions: a symplectic bi-Grassmannian representation of CFT$_4$ Wightman correlators. Working in Klein space with off-shell spinor-helicity variables, we show that correlators of $Δ= 2$ scalars and symmetric-traceless conserved currents are encoded by integrals over a pair of $n$-planes in a $2n$-dimensional symplectic vector space. These planes are constrained to be mutually symplectically orthogonal and aligned with the external kinematics. Conformal invariance, momentum conservation, and little-group covariance all follow geometrically from this structure. We derive all two- and three-point functions involving scalars, fermions, conserved currents, and stress tensors. As a non-trivial test, we show that the construction reproduces the full set of independent conformally invariant structures of $\\langle JJJ\\rangle$ and $\\langle TTT\\rangle$ in CFT$_4$. The resulting expressions are considerably more compact than their momentum-space counterparts. They also make manifest the double copy between Yang--Mills $\\langle JJJ \\rangle$ and Einstein-gravity $\\langle TTT \\rangle$. We further present a helicity-basis reformulation that makes the GL(1,R) and SL(2,R) weights of individual helicity components explicit. This basis also provides a natural starting point for a twistor-space formulation of the correlators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.06811",
  "author_total": 3,
  "authors": [
    {
      "name": "Aswini Bala"
    },
    {
      "name": "Sachin Jain"
    },
    {
      "name": "Dhruva K. S"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mbzcrb43mmek.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.06811",
  "fulltext_url": null,
  "id": "1mbzcrb43mmek",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.06811",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7160855879",
  "pdf_url": "https://arxiv.org/pdf/2605.06811",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mbzcrb43mmek.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2605.06811",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.06811"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Conformal Grassmannian: A Symplectic Bi-Grassmannian for $CFT_ 4$ Correlators",
  "title_text": "The Conformal Grassmannian: A Symplectic Bi-Grassmannian for CFT_4 Correlators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/1mbzcrb43mmek",
  "venue": "arXiv",
  "versions": []
}