{
  "id": "2308.05044",
  "version": "v1",
  "published": "2023-08-09T16:18:24.000Z",
  "updated": "2023-08-09T16:18:24.000Z",
  "title": "Cyclic products of higher-genus Szegö kernels, modular tensors and polylogarithms",
  "authors": [
    "Eric D'Hoker",
    "Martijn Hidding",
    "Oliver Schlotterer"
  ],
  "comment": "5.5 + 1.5 pages",
  "categories": [
    "hep-th",
    "math.AG",
    "math.NT"
  ],
  "abstract": "A wealth of information on multiloop string amplitudes is encoded in two-point functions of worldsheet fermions known as Szeg\\\"o kernels. Cyclic products of an arbitrary number of Szeg\\\"o kernels for any even spin structure $\\delta$ on a Riemann surface of arbitrary genus are decomposed into linear combinations of modular tensors on moduli space that carry all the dependence on the spin structure $\\delta$. The coefficients in these linear combinations are independent of $\\delta$, carry all the dependence on the marked points and are composed of the integration kernels of higher-genus polylogarithms constructed in arXiv:2306.08644. The conditions under which these modular tensors are locally holomorphic on moduli space are determined and explicit formulas for the special case of genus two are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-09T16:18:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular tensors",
      "cyclic products",
      "higher-genus",
      "polylogarithms",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}