{
  "abstract": "We study a link-based retarded scalar propagator on causal sets sprinkled into $2+1$-dimensional Minkowski, anti-de Sitter, and de Sitter spacetimes. The construction is based on the squared link matrix $\\mathbf{L}^2$, whose expectation value counts two-link paths between fixed endpoints. In the high-density limit, the dominant contribution localizes near the intersection of the null boundaries of the Alexandrov interval, and the flat-space normalization remains unchanged in constant curvature. The resulting kernels agree with the corresponding continuum Klein-Gordon propagators for a nominally massless scalar with effective curvature coupling $ξ_{\\rm link}=1/6$. Since the conformal coupling in $2+1$ spacetime dimensions is $1/8$, this value is not a conformal-coupling effect. Together with link-based results in $1+1$ and $3+1$ dimensions, where the same coefficient $1/6$ appears, this suggests that the coupling may reflect an ultraviolet property of the link structure, reminiscent of the combination $(1/6-ξ)\\mathcal{R}$ in local heat-kernel expansions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26221",
  "author_total": 1,
  "authors": [
    {
      "name": "Arsim Kastrati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ea2jcrswht3m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26221",
  "fulltext_url": null,
  "id": "9ea2jcrswht3m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26221",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3109|Noncommutative and Quantum Gravity Theories"
    ]
  ],
  "openalex": "W7223036076",
  "pdf_url": "https://arxiv.org/pdf/2610.26221",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ea2jcrswht3m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26221",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26221"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Construction of Causal Set Propagators in $2+1$-Dimensional Constant-Curvature Spacetimes from Two-Link Paths",
  "title_text": "Construction of Causal Set Propagators in 2+1-Dimensional Constant-Curvature Spacetimes from Two-Link Paths",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/9ea2jcrswht3m",
  "venue": "arXiv",
  "versions": []
}