{
  "abstract": "MHV form factors of the chiral stress-tensor multiplet in planar $\\mathcal N=4$ super Yang-Mills theory are dual to periodic null Wilson loops. We propose a periodic $\\bar q$ equation for the MHV and higher-helicity sectors at vanishing fermionic monodromy. The equation relates kinematic derivatives of $\\mathrm N^k\\mathrm{MHV}$ form factors to collinear integrals of $\\mathrm N^{k+1}\\mathrm{MHV}$ form factors with one additional external particle, providing a recursive relation in loop order. In periodic momentum supertwistors, it has the same collinear-integral form as the two dotted components of the amplitude $\\bar Q$ equation, with coefficient $Γ_{\\rm cusp}/4$, despite the absence of ordinary dual conformal invariance at fixed operator momentum. For parity-even scalar MHV remainders, combining the equation with its parity image supplies all directions of the kinematic differential. We verify the equation analytically for the one-loop four-point NMHV form factor and reconstruct the two-loop three-point MHV remainder at function level. Further two-loop MHV tests give numerical agreement with derivatives of the known four-point remainder at a fixed kinematic configuration, and for five points, all six chiral derivatives agree exactly at symbol level for a one-parameter family of kinematics. The structure of the collinear source further gives all-loop predictions for MHV last entries, consistent with known results and form a space of dimension $n(2n-5)$. The periodic Wilson-loop picture also motivates an all-loop derivation. Using the form-factor OPE, we extract the one-loop correction to the fermion energy from the logarithmic source and recover its vanishing at zero momentum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30633",
  "author_total": 2,
  "authors": [
    {
      "name": "Song He"
    },
    {
      "name": "Jiahao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nzq0c6zgpn39.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30633",
  "fulltext_url": null,
  "id": "0nzq0c6zgpn39",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30633",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223406651",
  "pdf_url": "https://arxiv.org/pdf/2610.30633",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nzq0c6zgpn39.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30633",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30633"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "A periodic $\\bar q$ equation for form factors",
  "title_text": "A periodic q̅ equation for form factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/0nzq0c6zgpn39",
  "venue": "arXiv",
  "versions": []
}