{
  "id": "2403.18078",
  "version": "v1",
  "published": "2024-03-26T19:58:25.000Z",
  "updated": "2024-03-26T19:58:25.000Z",
  "title": "Advanced tools for basis decompositions of genus-one string integrals",
  "authors": [
    "Yong Zhang"
  ],
  "comment": "44+9 pages, 9 figures",
  "categories": [
    "hep-th"
  ],
  "abstract": "In string theories, one-loop scattering amplitudes are characterized by integrals over genus-one surfaces using the Kronecker-Eisenstein series. A recent methodology proposed a genus-one basis formed from products of these series of chain topologies. A prior work further deconstructed cyclic products of the Kronecker-Eisenstein series on this basis. Building on it, our study further employs advanced and comprehensive combinatorial techniques to decompose more general genus-one integrands including a product of an arbitrary number of cyclic products of Kronecker-Eisenstein series, supplemented by {\\tt Mathematica} codes. Our insights enhance the understanding of multiparticle amplitudes across various string theories and illuminate loop-level parallels with string tree-level amplitudes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-26T19:58:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "genus-one string integrals",
      "basis decompositions",
      "advanced tools",
      "kronecker-eisenstein series",
      "cyclic products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}